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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.17895">arXiv:2412.17895</a> <span> [<a href="https://arxiv.org/pdf/2412.17895">pdf</a>, <a href="https://arxiv.org/format/2412.17895">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> A landscape of 4d N=1 SCFTs with a=c </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.17895v1-abstract-short" style="display: inline;"> We study a landscape of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with identical central charges. These theories are obtained by renormalization group flows triggered by supersymmetry-preserving superpotential deformations of the $\mathcal{N}=1$ gauging of the flavor symmetry of a collection of $\mathcal{N}=2$ $\mathcal{D}_p(G)$ Argyres--Douglas SCFTs. In this work, we… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.17895v1-abstract-full').style.display = 'inline'; document.getElementById('2412.17895v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.17895v1-abstract-full" style="display: none;"> We study a landscape of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with identical central charges. These theories are obtained by renormalization group flows triggered by supersymmetry-preserving superpotential deformations of the $\mathcal{N}=1$ gauging of the flavor symmetry of a collection of $\mathcal{N}=2$ $\mathcal{D}_p(G)$ Argyres--Douglas SCFTs. In this work, we focus on the fixed points in the landscape of the $SU(3)$ gauging of three copies of the $\mathcal{D}_2(SU(3)) = H_2$ theory together with an adjoint-valued chiral multiplet. We catalogue the network of $a = c$ fixed points, and, along the way, we find a variety of dualities and instances of supersymmetry enhancement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.17895v1-abstract-full').style.display = 'none'; document.getElementById('2412.17895v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">54 pages + references, 3 figures, and 3 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-171 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.15202">arXiv:2412.15202</a> <span> [<a href="https://arxiv.org/pdf/2412.15202">pdf</a>, <a href="https://arxiv.org/format/2412.15202">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> A Pathway to Decay and Fission of Orthosymplectic Quiver Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Mansi%2C+L">Lorenzo Mansi</a>, <a href="/search/hep-th?searchtype=author&query=Sperling%2C+M">Marcus Sperling</a>, <a href="/search/hep-th?searchtype=author&query=Zhong%2C+Z">Zhenghao Zhong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.15202v1-abstract-short" style="display: inline;"> We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic 3d $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.15202v1-abstract-full').style.display = 'inline'; document.getElementById('2412.15202v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.15202v1-abstract-full" style="display: none;"> We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic 3d $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism $\mathfrak{su}(4) \cong \mathfrak{so}(6)$, we validate our algorithm via the 3d mirror of 4d theories of class $\mathcal{S}$ of such type. This comparison involves moduli spaces that admit both orthosymplectic and unitary quiver realisations, the latter being well-understood via standard techniques such as Decay and Fission. Higgsing on the Coulomb branch of the 3d mirror or magnetic quiver translates to Higgs branch renormalization group flows of the corresponding higher-dimensional SCFTs. Thus, we benchmark our method via Higgsing 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton theories, predicting novel Higgsing patterns involving products of interacting fixed points, and class $\mathcal{S}$ theories of type $\mathfrak{so}(2N)$, demonstrating Higgsing to products of theories of types specified by Levi subalgebras of $\mathfrak{so}(2N)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.15202v1-abstract-full').style.display = 'none'; document.getElementById('2412.15202v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages, 10 figure, 3 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-185, UWThPh 2024-26 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.02126">arXiv:2409.02126</a> <span> [<a href="https://arxiv.org/pdf/2409.02126">pdf</a>, <a href="https://arxiv.org/format/2409.02126">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Detecting Homeomorphic 3-manifolds via Graph Neural Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Mansi%2C+L">Lorenzo Mansi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.02126v1-abstract-short" style="display: inline;"> Motivated by the enumeration of the BPS spectra of certain 3d $\mathcal{N}=2$ supersymmetric quantum field theories, obtained from the compactification of 6d superconformal field theories on three-manifolds, we study the homeomorphism problem for a class of graph-manifolds using Graph Neural Network techniques. Utilizing the JSJ decomposition, a unique representation via a plumbing graph is extrac… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.02126v1-abstract-full').style.display = 'inline'; document.getElementById('2409.02126v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.02126v1-abstract-full" style="display: none;"> Motivated by the enumeration of the BPS spectra of certain 3d $\mathcal{N}=2$ supersymmetric quantum field theories, obtained from the compactification of 6d superconformal field theories on three-manifolds, we study the homeomorphism problem for a class of graph-manifolds using Graph Neural Network techniques. Utilizing the JSJ decomposition, a unique representation via a plumbing graph is extracted from a graph-manifold. Homeomorphic graph-manifolds are related via a sequence of von Neumann moves on this graph; the algorithmic application of these moves can determine if two graphs correspond to homeomorphic graph-manifolds in super-polynomial time. However, by employing Graph Neural Networks (GNNs), the same problem can be addressed, at the cost of accuracy, in polynomial time. We build a dataset composed of pairs of plumbing graphs, together with a hidden label encoding whether the pair is homeomorphic. We train and benchmark a variety of network architectures within a supervised learning setting by testing different combinations of two convolutional layers (GEN, GCN, GAT, NNConv), followed by an aggregation layer and a classification layer. We discuss the strengths and weaknesses of the different GNNs for this homeomorphism problem. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.02126v1-abstract-full').style.display = 'none'; document.getElementById('2409.02126v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 3 figures, 2 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-122 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.14532">arXiv:2408.14532</a> <span> [<a href="https://arxiv.org/pdf/2408.14532">pdf</a>, <a href="https://arxiv.org/format/2408.14532">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Generalized symmetry constraints on deformed 4d (S)CFTs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.14532v1-abstract-short" style="display: inline;"> We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.14532v1-abstract-full').style.display = 'inline'; document.getElementById('2408.14532v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.14532v1-abstract-full" style="display: none;"> We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two $\mathcal{D}_3(SU(N))$ theories and $SU(N)$ gauge theory with two adjoints. We also repeat our analysis for a host of non-supersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.14532v1-abstract-full').style.display = 'none'; document.getElementById('2408.14532v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">78 pages + references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-125 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.02670">arXiv:2406.02670</a> <span> [<a href="https://arxiv.org/pdf/2406.02670">pdf</a>, <a href="https://arxiv.org/format/2406.02670">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Higgs Branch of 6d (1,0) SCFTs & LSTs with DE-type SUSY Enhancement </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Mansi%2C+L">Lorenzo Mansi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.02670v1-abstract-short" style="display: inline;"> We detail the Higgs branches of 6d $(1,0)$ superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6d $(2,0)$ SCFTs and LSTs of type DE. Generically, such theories are geometrically engineered in F-theory via a configuration of $(-2)$-curves, arranged in an (affine) DE-type Dynkin diagram, and supp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.02670v1-abstract-full').style.display = 'inline'; document.getElementById('2406.02670v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.02670v1-abstract-full" style="display: none;"> We detail the Higgs branches of 6d $(1,0)$ superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6d $(2,0)$ SCFTs and LSTs of type DE. Generically, such theories are geometrically engineered in F-theory via a configuration of $(-2)$-curves, arranged in an (affine) DE-type Dynkin diagram, and supporting special unitary gauge algebras; this describes the effective field theory on the tensor branch of the SCFT. For the Higgsable to D-type $(2,0)$ SCFTs/LSTs, there generically also exists a Type IIA brane description, involving a Neveu--Schwarz orientifold plane, which allows for the derivation of a magnetic quiver for the Higgs branch. These are 3d $\mathcal{N}=4$ unitary-orthosymplectic quivers whose Coulomb branch is isomorphic to the Higgs branch of the 6d theories. From this magnetic quiver, together with an extended quiver subtraction algorithm that we explain, the foliation structure of the Higgs branch as a symplectic singularity is unveiled. For this class of 6d SCFTs, we observe a simple rule, which we refer to as "slice subtraction," to read off the transverse slice in the foliation from the tensor branch. Based on this slice subtraction observation, we conjecture the transverse slices in the Higgsable to E-type $(2,0)$ Hasse diagram, where the SCFTs lack any known magnetic quiver for their Higgs branches. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.02670v1-abstract-full').style.display = 'none'; document.getElementById('2406.02670v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">64 pages, 20 figures, 6 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-079 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.13347">arXiv:2312.13347</a> <span> [<a href="https://arxiv.org/pdf/2312.13347">pdf</a>, <a href="https://arxiv.org/format/2312.13347">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Bestiary of 6d (1,0) SCFTs: Nilpotent Orbits and Anomalies </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.13347v2-abstract-short" style="display: inline;"> Many six-dimensional $(1,0)$ SCFTs are known to fall into families labelled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form global symmetries of a theory labelled by a nilpotent orbit $O$ of $\mathfrak{g}$ can be determined from the anomalies of the theory associated to the trivial n… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.13347v2-abstract-full').style.display = 'inline'; document.getElementById('2312.13347v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.13347v2-abstract-full" style="display: none;"> Many six-dimensional $(1,0)$ SCFTs are known to fall into families labelled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form global symmetries of a theory labelled by a nilpotent orbit $O$ of $\mathfrak{g}$ can be determined from the anomalies of the theory associated to the trivial nilpotent orbit (the parent theory), together with the data of $O$. In particular, knowledge of the tensor branch field theory is bypassed completely. We show that the known anomalies, previously determined from the geometric/atomic construction, are reproduced by analyzing the Nambu--Goldstone modes inside of the moment map associated to the $\mathfrak{g}$ flavor symmetry of the parent SCFT. This provides further evidence for the physics underlying the labelling of the SCFTs by nilpotent orbits. We remark on some consequences, such as the reinterpretation of the 6d $a$-theorem for such SCFTs in terms of group theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.13347v2-abstract-full').style.display = 'none'; document.getElementById('2312.13347v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">69 pages + exhaustive appendices, 6 figures, 25 tables; v2: journal version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-23-204, ZMP-HH/23-20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.12503">arXiv:2312.12503</a> <span> [<a href="https://arxiv.org/pdf/2312.12503">pdf</a>, <a href="https://arxiv.org/format/2312.12503">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Holographic duals of Higgsed $\mathcal{D}_p^b(BCD)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Couzens%2C+C">Christopher Couzens</a>, <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+Y">Yein Lee</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.12503v1-abstract-short" style="display: inline;"> We construct the AdS$_5$ holographic duals to all non-Lagrangian 4d $\mathcal{N}=2$ superconformal field theories of Argyres--Douglas type, namely, $\mathcal{D}_p^{\,b}(G)$, arising from class $\mathcal{S}$ of classical type involving irregular punctures of regular semi-simple type. The 11d supergravity duals contain an internal space of the form of a fibered product of a disc with a squashed and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.12503v1-abstract-full').style.display = 'inline'; document.getElementById('2312.12503v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.12503v1-abstract-full" style="display: none;"> We construct the AdS$_5$ holographic duals to all non-Lagrangian 4d $\mathcal{N}=2$ superconformal field theories of Argyres--Douglas type, namely, $\mathcal{D}_p^{\,b}(G)$, arising from class $\mathcal{S}$ of classical type involving irregular punctures of regular semi-simple type. The 11d supergravity duals contain an internal space of the form of a fibered product of a disc with a squashed and fibered four-sphere and includes orbifold projections which depend on the type of twist lines/outer-automorphism twists in the class $\mathcal{S}$ theory. We verify the holographic duality by determining and matching the anomalies (including the central charges $a$ and $c$ and the flavor central charges) at leading and subleading orders. The Higgs branch of the conformal field theory is described via Higgsing by a nilpotent orbit of a classical Lie algebra; we find the exact closed form formulae for the central charges for every Higgsing. We prove that in the supergravity duals, constraints on the type of partitions associated to allowable Higgsings are enforced by the consistency condition known as the t-rule. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.12503v1-abstract-full').style.display = 'none'; document.getElementById('2312.12503v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">49 pages + references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2023-053; DESY-23-078 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.05306">arXiv:2312.05306</a> <span> [<a href="https://arxiv.org/pdf/2312.05306">pdf</a>, <a href="https://arxiv.org/format/2312.05306">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Higgs Branch of Heterotic LSTs: Hasse Diagrams and Generalized Symmetries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Mansi%2C+L">Lorenzo Mansi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.05306v2-abstract-short" style="display: inline;"> We study the Higgs branches of the 6d $(1,0)$ little string theories that live on the worldvolume of NS5-branes probing an ADE-singularity in the heterotic $E_8 \times E_8$ and $\mathrm{Spin}(32)/\mathbb{Z}_2$ string theories. On the $E_8 \times E_8$ side, such LSTs are obtained via fusion of orbi-instanton SCFTs. For the $\mathbb{C}^2/\mathbb{Z}_K$ orbifolds, we determine a magnetic quiver for th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.05306v2-abstract-full').style.display = 'inline'; document.getElementById('2312.05306v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.05306v2-abstract-full" style="display: none;"> We study the Higgs branches of the 6d $(1,0)$ little string theories that live on the worldvolume of NS5-branes probing an ADE-singularity in the heterotic $E_8 \times E_8$ and $\mathrm{Spin}(32)/\mathbb{Z}_2$ string theories. On the $E_8 \times E_8$ side, such LSTs are obtained via fusion of orbi-instanton SCFTs. For the $\mathbb{C}^2/\mathbb{Z}_K$ orbifolds, we determine a magnetic quiver for the Higgs branch from the alternative Type IIA brane system engineering the LST; we show that the magnetic quiver obtained in this way is the same as the Coulomb gauging of the 3d mirrors associated to the orbi-instanton building blocks. Using quiver subtraction, we determine the Hasse diagram of Higgs branch RG flows between the LSTs, and we analyze how the structure constants of the generalized global symmetries vary along the edges of the Hasse diagram. From the Hasse diagram of the Higgs branch, we are immediately able to identify LSTs with the same T-duality-invariant properties, and thus to propose candidate T-dual pairs. We perform a similar analysis of the Higgs branch Hasse diagram and putative T-dual families for particular $E_6$-orbifold LSTs by taking advantage of a duality between a rank zero orbi-instanton theory and a rank one conformal matter theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.05306v2-abstract-full').style.display = 'none'; document.getElementById('2312.05306v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">68 pages, 16 figures, 8 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-23-199 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.11783">arXiv:2306.11783</a> <span> [<a href="https://arxiv.org/pdf/2306.11783">pdf</a>, <a href="https://arxiv.org/format/2306.11783">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Intermediate Defect Groups, Polarization Pairs, and Non-invertible Duality Defects </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Yu%2C+X">Xingyang Yu</a>, <a href="/search/hep-th?searchtype=author&query=Zhang%2C+H+Y">Hao Y. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.11783v1-abstract-short" style="display: inline;"> Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing non-invertible duality defects in theories in $2k$ spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their $(k-1)$-form defect g… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.11783v1-abstract-full').style.display = 'inline'; document.getElementById('2306.11783v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.11783v1-abstract-full" style="display: none;"> Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing non-invertible duality defects in theories in $2k$ spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their $(k-1)$-form defect groups are concerned, including their $(k-1)$-form symmetries, global structures (including discrete $胃$-angle), and local counterterms. Using the associated symmetry TFT, we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging $(k-1)$-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the $(k-1)$-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building non-invertible symmetries of absolute QFTs. A large class of known examples, e.g., non-invertible defects in 4D $\mathcal{N}=4$ super-Yang--Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of non-invertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from Type IIB string theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.11783v1-abstract-full').style.display = 'none'; document.getElementById('2306.11783v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">48 pages + appendices, 7 figures, 2 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-23-079; UPR-1323-T </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.06622">arXiv:2302.06622</a> <span> [<a href="https://arxiv.org/pdf/2302.06622">pdf</a>, <a href="https://arxiv.org/format/2302.06622">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.130.231601">10.1103/PhysRevLett.130.231601 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Emergent N=4 supersymmetry from N=1 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.06622v3-abstract-short" style="display: inline;"> We discover a four-dimensional $\mathcal{N}=1$ supersymmetric field theory that is dual to the $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(2n+1)$ for each $n$. The dual theory is constructed through the diagonal gauging of the $SU(2n+1)$ flavor symmetry of three copies of a strongly-coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.06622v3-abstract-full').style.display = 'inline'; document.getElementById('2302.06622v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.06622v3-abstract-full" style="display: none;"> We discover a four-dimensional $\mathcal{N}=1$ supersymmetric field theory that is dual to the $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(2n+1)$ for each $n$. The dual theory is constructed through the diagonal gauging of the $SU(2n+1)$ flavor symmetry of three copies of a strongly-coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows in the infrared to a strongly-coupled $\mathcal{N}=1$ SCFT that lies on the same conformal manifold as $\mathcal{N}=4$ super Yang-Mills with gauge group $SU(2n+1)$. Our construction provides a hint on why certain $\mathcal{N}=1,2$ SCFTs have identical central charges ($a=c$). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.06622v3-abstract-full').style.display = 'none'; document.getElementById('2302.06622v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 1 figure, v3: Journal published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2023-005; DESY-23-021 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 130, 231601 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.11983">arXiv:2212.11983</a> <span> [<a href="https://arxiv.org/pdf/2212.11983">pdf</a>, <a href="https://arxiv.org/format/2212.11983">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.107.106005">10.1103/PhysRevD.107.106005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Isomorphisms of 4d N=2 SCFTs from 6d </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Distler%2C+J">Jacques Distler</a>, <a href="/search/hep-th?searchtype=author&query=Elliot%2C+G">Grant Elliot</a>, <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.11983v1-abstract-short" style="display: inline;"> There exist 4d $\mathcal{N}=2$ SCFTs in class $\mathcal{S}$ which have different constructions as punctured Riemann surfaces, but which nevertheless appear to describe the same physics. Some of these class $\mathcal{S}$ theories have an alternative construction as torus-compactifications of 6d $(1,0)$ SCFTs. We demonstrate that the 6d SCFTs are isomorphic. Each 6d SCFT in question can be obtained… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11983v1-abstract-full').style.display = 'inline'; document.getElementById('2212.11983v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.11983v1-abstract-full" style="display: none;"> There exist 4d $\mathcal{N}=2$ SCFTs in class $\mathcal{S}$ which have different constructions as punctured Riemann surfaces, but which nevertheless appear to describe the same physics. Some of these class $\mathcal{S}$ theories have an alternative construction as torus-compactifications of 6d $(1,0)$ SCFTs. We demonstrate that the 6d SCFTs are isomorphic. Each 6d SCFT in question can be obtained from a parent 6d SCFT by Higgs branch renormalization group flow, and the parent theory possesses a discrete symmetry under which the relevant Higgs branch flows are exchanged. The existence of this discrete symmetry, which may be embedded in an enhanced continuous symmetry, proves that the original pair of class $\mathcal{S}$ theories are, in fact, isomorphic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11983v1-abstract-full').style.display = 'none'; document.getElementById('2212.11983v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">44 pages + references, 6 figures, and 5 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2022-044; DESY-22-201; UTWI 17-2022 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.06497">arXiv:2210.06497</a> <span> [<a href="https://arxiv.org/pdf/2210.06497">pdf</a>, <a href="https://arxiv.org/format/2210.06497">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Operator spectroscopy for 4d SCFTs with a=c </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.06497v1-abstract-short" style="display: inline;"> We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.1… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.06497v1-abstract-full').style.display = 'inline'; document.getElementById('2210.06497v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.06497v1-abstract-full" style="display: none;"> We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting SCFTs with $a=c$ in the infrared. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.06497v1-abstract-full').style.display = 'none'; document.getElementById('2210.06497v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">38 pages + appendix + references, and 6 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2022-035; DESY-22-152 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.02272">arXiv:2208.02272</a> <span> [<a href="https://arxiv.org/pdf/2208.02272">pdf</a>, <a href="https://arxiv.org/format/2208.02272">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2023.116250">10.1016/j.nuclphysb.2023.116250 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Super-Spin Chains for 6D SCFTs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.02272v2-abstract-short" style="display: inline;"> Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.02272v2-abstract-full').style.display = 'inline'; document.getElementById('2208.02272v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.02272v2-abstract-full" style="display: none;"> Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$ is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver structures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.02272v2-abstract-full').style.display = 'none'; document.getElementById('2208.02272v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages + appendices, 7 figures. v2: minor clarifications; published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-22-132 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.05764">arXiv:2207.05764</a> <span> [<a href="https://arxiv.org/pdf/2207.05764">pdf</a>, <a href="https://arxiv.org/format/2207.05764">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.106.106021">10.1103/PhysRevD.106.106021 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higgs, Coulomb, and Hall-Littlewood </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Sacchi%2C+M">Matteo Sacchi</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.05764v1-abstract-short" style="display: inline;"> The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.05764v1-abstract-full').style.display = 'inline'; document.getElementById('2207.05764v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.05764v1-abstract-full" style="display: none;"> The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more $\mathbb{Z}_2$-twisted punctures, they do not match. We construct 3d mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4d theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the $\hat{D}_4(SU(2n+1))$ theories, have Hall--Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with non-empty Higgs branch, including $\mathcal{N}\ge 3$ SCFTs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.05764v1-abstract-full').style.display = 'none'; document.getElementById('2207.05764v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">49 pages + appendices + references, 20 figures, and 5 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2022-024; DESY-22-110 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review D 106, no.10, 106021 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.03411">arXiv:2205.03411</a> <span> [<a href="https://arxiv.org/pdf/2205.03411">pdf</a>, <a href="https://arxiv.org/format/2205.03411">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.106.066003">10.1103/PhysRevD.106.066003 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Zhang%2C+H+Y">Hao Y. Zhang</a>, <a href="/search/hep-th?searchtype=author&query=Zoccarato%2C+G">Gianluca Zoccarato</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.03411v2-abstract-short" style="display: inline;"> The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.03411v2-abstract-full').style.display = 'inline'; document.getElementById('2205.03411v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.03411v2-abstract-full" style="display: none;"> The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N} = 2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N} = 2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N} = 2$ SCFTs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.03411v2-abstract-full').style.display = 'none'; document.getElementById('2205.03411v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">69 pages + appendices, 2 figures, 9 tables, 1 attached Mathematica notebook; v2: PRD version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH 2022-074, DESY-22-069 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.08829">arXiv:2203.08829</a> <span> [<a href="https://arxiv.org/pdf/2203.08829">pdf</a>, <a href="https://arxiv.org/format/2203.08829">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.106.066011">10.1103/PhysRevD.106.066011 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Distler%2C+J">Jacques Distler</a>, <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.08829v2-abstract-short" style="display: inline;"> We provide a new extension to the geometric construction of 6d $(1,0)$ SCFTs that encapsulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d $(1,0)$ SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nil… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.08829v2-abstract-full').style.display = 'inline'; document.getElementById('2203.08829v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.08829v2-abstract-full" style="display: none;"> We provide a new extension to the geometric construction of 6d $(1,0)$ SCFTs that encapsulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d $(1,0)$ SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nilpotent Higgsing of $(\mathfrak{so}_{4k}, \mathfrak{so}_{4k})$ conformal matter; we propose a method to predict at which conformal dimension the Higgs branch operators of the two theories differ via augmenting the tensor branch description with the Higgs branch chiral ring generators of the building block theories. Torus compactifications of these 6d $(1,0)$ SCFTs give rise to 4d $\mathcal{N}=2$ SCFTs of class $\mathcal{S}$ and the Higgs branch of such 4d theories are captured via the Hall--Littlewood index. We confirm that the resulting 4d theories indeed differ in their spectra in the predicted conformal dimension from their Hall--Littlewood indices. We highlight how this ambiguity in the tensor branch description arises beyond the very even nilpotent Higgsing of $(\mathfrak{so}_{4k}, \mathfrak{so}_{4k})$ conformal matter, and hence should be understood for more general classes of 6d $(1,0)$ SCFTs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.08829v2-abstract-full').style.display = 'none'; document.getElementById('2203.08829v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages+references, 1 figure, Journal published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2022-012, DESY-22-044, UTTG 03-2022 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D 106 (2022) 6, 066011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.12092">arXiv:2111.12092</a> <span> [<a href="https://arxiv.org/pdf/2111.12092">pdf</a>, <a href="https://arxiv.org/format/2111.12092">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.105.126006">10.1103/PhysRevD.105.126006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Infinitely many 4d N=1 SCFTs with a=c </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lee%2C+K">Ki-Hong Lee</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.12092v3-abstract-short" style="display: inline;"> We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.12092v3-abstract-full').style.display = 'inline'; document.getElementById('2111.12092v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.12092v3-abstract-full" style="display: none;"> We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.12092v3-abstract-full').style.display = 'none'; document.getElementById('2111.12092v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">43 pages+references, 11 figures, 5 tables, Journal published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2021-040; DESY 21-190; </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D 105 (2022) 12, 126006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.02453">arXiv:2111.02453</a> <span> [<a href="https://arxiv.org/pdf/2111.02453">pdf</a>, <a href="https://arxiv.org/format/2111.02453">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.105.046006">10.1103/PhysRevD.105.046006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Bootstrapping (D, D) Conformal Matter </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.02453v1-abstract-short" style="display: inline;"> We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.02453v1-abstract-full').style.display = 'inline'; document.getElementById('2111.02453v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.02453v1-abstract-full" style="display: none;"> We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel OPE selection rules involving type-$\mathcal{B}$ multiplets. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.02453v1-abstract-full').style.display = 'none'; document.getElementById('2111.02453v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21-165 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.12579">arXiv:2106.12579</a> <span> [<a href="https://arxiv.org/pdf/2106.12579">pdf</a>, <a href="https://arxiv.org/format/2106.12579">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.104.105005">10.1103/PhysRevD.104.105005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Song%2C+J">Jaewon Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.12579v2-abstract-short" style="display: inline;"> We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\widehat螕(G)$ labeled by a pair of simply-laced Lie groups $螕$ and $G$. They are constructed out of gauging a number of $\mathcal{D}_p(G)$ and $(G, G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $螕= D_4, E_6, E_7, E_8$ and some special choices of $G$, the result… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.12579v2-abstract-full').style.display = 'inline'; document.getElementById('2106.12579v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.12579v2-abstract-full" style="display: none;"> We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\widehat螕(G)$ labeled by a pair of simply-laced Lie groups $螕$ and $G$. They are constructed out of gauging a number of $\mathcal{D}_p(G)$ and $(G, G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $螕= D_4, E_6, E_7, E_8$ and some special choices of $G$, the resulting theories have identical central charges $(a=c)$ without taking any large $N$ limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of $\mathcal{N}=4$ super Yang--Mills theory upon rescaling fugacities. Especially, we find that the Schur index of $\widehat{D}_4(SU(N))$ theory for $N$ odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasi-modular. For generic choices of $螕$ and $G$, it can be regarded as a generalization of the affine quiver gauge theory obtained from $D3$-branes probing an ALE singularity of type $螕$. We also comment on a tantalizing connection regarding the theories labeled by $螕$ in the Deligne--Cvitanovi膰 exceptional series. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.12579v2-abstract-full').style.display = 'none'; document.getElementById('2106.12579v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">33pages+appendix, 8 tables, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2021-026 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 104 (2021) 105005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.11990">arXiv:2106.11990</a> <span> [<a href="https://arxiv.org/pdf/2106.11990">pdf</a>, <a href="https://arxiv.org/format/2106.11990">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.106.086003">10.1103/PhysRevD.106.086003 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Kang%2C+M+J">Monica Jinwoo Kang</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.11990v2-abstract-short" style="display: inline;"> We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is iden… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.11990v2-abstract-full').style.display = 'inline'; document.getElementById('2106.11990v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.11990v2-abstract-full" style="display: none;"> We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.11990v2-abstract-full').style.display = 'none'; document.getElementById('2106.11990v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">54 pages + references, 10 tables, 8 figures, Journal published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CALT-TH-2021-001 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D 106 (2022) 8, 086003 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.10090">arXiv:2009.10090</a> <span> [<a href="https://arxiv.org/pdf/2009.10090">pdf</a>, <a href="https://arxiv.org/format/2009.10090">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.103.086013">10.1103/PhysRevD.103.086013 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> S-folds, String Junctions, and 4D $\mathcal{N} = 2$ SCFTs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Rochais%2C+T+B">Thomas B. Rochais</a>, <a href="/search/hep-th?searchtype=author&query=Zhang%2C+H+Y">Hao Y. Zhang</a>, <a href="/search/hep-th?searchtype=author&query=Zoccarato%2C+G">Gianluca Zoccarato</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.10090v1-abstract-short" style="display: inline;"> S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D $\mathcal{N} = 3$ SCFTs and have also recently been used to realize examples of 4D $\mathcal{N} = 2$ SCFTs. In this paper we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S-fold. We develop an S-fo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.10090v1-abstract-full').style.display = 'inline'; document.getElementById('2009.10090v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.10090v1-abstract-full" style="display: none;"> S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D $\mathcal{N} = 3$ SCFTs and have also recently been used to realize examples of 4D $\mathcal{N} = 2$ SCFTs. In this paper we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S-fold. We develop an S-fold generalization of orientifold projection which applies to non-perturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the S-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D $\mathcal{N} = 2$ SCFTs. Furthermore this provides a prescription for how to define F-theory in the presence of S-folds with discrete torsion. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.10090v1-abstract-full').style.display = 'none'; document.getElementById('2009.10090v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">49 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 086013 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.07262">arXiv:2007.07262</a> <span> [<a href="https://arxiv.org/pdf/2007.07262">pdf</a>, <a href="https://arxiv.org/format/2007.07262">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2021.115401">10.1016/j.nuclphysb.2021.115401 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.07262v4-abstract-short" style="display: inline;"> Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sec… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.07262v4-abstract-full').style.display = 'inline'; document.getElementById('2007.07262v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.07262v4-abstract-full" style="display: none;"> Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a $\mathbb{C}^{2}/\mathbb{Z}_{K}$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XXX_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XXX_{s}$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.07262v4-abstract-full').style.display = 'none'; document.getElementById('2007.07262v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v4: 52 pages, 5 figures, typos corrected</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.09128">arXiv:1909.09128</a> <span> [<a href="https://arxiv.org/pdf/1909.09128">pdf</a>, <a href="https://arxiv.org/format/1909.09128">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP03(2020)052">10.1007/JHEP03(2020)052 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Apruzzi%2C+F">Fabio Apruzzi</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Wang%2C+Y">Yi-Nan Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1909.09128v4-abstract-short" style="display: inline;"> In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this pape… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.09128v4-abstract-full').style.display = 'inline'; document.getElementById('1909.09128v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.09128v4-abstract-full" style="display: none;"> In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.09128v4-abstract-full').style.display = 'none'; document.getElementById('1909.09128v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">146 pages, lots of figures, v2: typos corrected, v3: JHEP published version, v4: typo in def 3.1 fixed</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.02768">arXiv:1908.02768</a> <span> [<a href="https://arxiv.org/pdf/1908.02768">pdf</a>, <a href="https://arxiv.org/format/1908.02768">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP11(2019)164">10.1007/JHEP11(2019)164 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Fuchs%2C+M">Michael Fuchs</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.02768v2-abstract-short" style="display: inline;"> For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks u… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.02768v2-abstract-full').style.display = 'inline'; document.getElementById('1908.02768v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.02768v2-abstract-full" style="display: none;"> For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.02768v2-abstract-full').style.display = 'none'; document.getElementById('1908.02768v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages, ancillary Mathematica notebook listing all block coefficients; minor corrections, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IFT-UAM/CSIC-19-112 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.05404">arXiv:1907.05404</a> <span> [<a href="https://arxiv.org/pdf/1907.05404">pdf</a>, <a href="https://arxiv.org/format/1907.05404">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP11(2019)068">10.1007/JHEP11(2019)068 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Apruzzi%2C+F">Fabio Apruzzi</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Wang%2C+Y">Yi-Nan Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1907.05404v3-abstract-short" style="display: inline;"> We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi--Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d $\mathcal{N}=(1,0)$ SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.05404v3-abstract-full').style.display = 'inline'; document.getElementById('1907.05404v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.05404v3-abstract-full" style="display: none;"> We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi--Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d $\mathcal{N}=(1,0)$ SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi--Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.05404v3-abstract-full').style.display = 'none'; document.getElementById('1907.05404v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">125 pages, 26 figures; v3: typos fixed</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.11820">arXiv:1906.11820</a> <span> [<a href="https://arxiv.org/pdf/1906.11820">pdf</a>, <a href="https://arxiv.org/format/1906.11820">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2019.135077">10.1016/j.physletb.2019.135077 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> 5d Superconformal Field Theories and Graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Apruzzi%2C+F">Fabio Apruzzi</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Wang%2C+Y">Yi-Nan Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1906.11820v2-abstract-short" style="display: inline;"> We propose a graph-theoretic description to determine and characterize 5d superconformal field theories (SCFTs) that arise as circle reductions of 6d $\mathcal{N} = (1,0)$ SCFTs. Each 5d SCFT is captured by a graph, called a Combined Fiber Diagram (CFD). Transitions between CFDs encode mass deformations that trigger flows between SCFTs. In this way, the complete set of descendants of a given 6d th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.11820v2-abstract-full').style.display = 'inline'; document.getElementById('1906.11820v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.11820v2-abstract-full" style="display: none;"> We propose a graph-theoretic description to determine and characterize 5d superconformal field theories (SCFTs) that arise as circle reductions of 6d $\mathcal{N} = (1,0)$ SCFTs. Each 5d SCFT is captured by a graph, called a Combined Fiber Diagram (CFD). Transitions between CFDs encode mass deformations that trigger flows between SCFTs. In this way, the complete set of descendants of a given 6d theory are obtained from a single marginal CFD. The graphs encode key physical information like the superconformal flavor symmetry and BPS states. As an illustration, we ascertain the aforementioned data associated to all the 5d SCFTs descending from 6d minimal $(E_6, E_6)$ and $(D_k, D_k)$ conformal matter for any $k$. This includes predictions for thus far unknown flavor symmetry enhancements. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.11820v2-abstract-full').style.display = 'none'; document.getElementById('1906.11820v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures. Supplementary material available here: https://people.maths.ox.ac.uk/schafernamek/CFD</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.02212">arXiv:1906.02212</a> <span> [<a href="https://arxiv.org/pdf/1906.02212">pdf</a>, <a href="https://arxiv.org/format/1906.02212">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.101.026015">10.1103/PhysRevD.101.026015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> T-Branes and $G_2$ Backgrounds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Barbosa%2C+R">Rodrigo Barbosa</a>, <a href="/search/hep-th?searchtype=author&query=Cveti%C4%8D%2C+M">Mirjam Cveti膷</a>, <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Torres%2C+E">Ethan Torres</a>, <a href="/search/hep-th?searchtype=author&query=Zoccarato%2C+G">Gianluca Zoccarato</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1906.02212v2-abstract-short" style="display: inline;"> Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.02212v2-abstract-full').style.display = 'inline'; document.getElementById('1906.02212v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.02212v2-abstract-full" style="display: none;"> Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by non-commuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure "hidden" in T-branes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.02212v2-abstract-full').style.display = 'none'; document.getElementById('1906.02212v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: 47 pages, 3 figures, references and clarifications added, typos corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 101, 026015 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1901.10489">arXiv:1901.10489</a> <span> [<a href="https://arxiv.org/pdf/1901.10489">pdf</a>, <a href="https://arxiv.org/format/1901.10489">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/prop.201900071">10.1002/prop.201900071 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Pixelated Dark Energy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Sakstein%2C+J">Jeremy Sakstein</a>, <a href="/search/hep-th?searchtype=author&query=Zoccarato%2C+G">Gianluca Zoccarato</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1901.10489v1-abstract-short" style="display: inline;"> We study the phenomenology of a recent string construction with a quantum mechanically stable dark energy. A mild supersymmetry protects the vacuum energy but also allows $O(10 - 100)$ TeV scale superpartner masses. The construction is holographic in the sense that the 4D spacetime is generated from "pixels" originating from five-branes wrapped over metastable five-cycles of the compactification.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1901.10489v1-abstract-full').style.display = 'inline'; document.getElementById('1901.10489v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1901.10489v1-abstract-full" style="display: none;"> We study the phenomenology of a recent string construction with a quantum mechanically stable dark energy. A mild supersymmetry protects the vacuum energy but also allows $O(10 - 100)$ TeV scale superpartner masses. The construction is holographic in the sense that the 4D spacetime is generated from "pixels" originating from five-branes wrapped over metastable five-cycles of the compactification. The cosmological constant scales as $螞\sim 1/N$ in the pixel number. An instability in the construction leads to cosmic expansion. This also causes more five-branes to wind up in the geometry, leading to a slowly decreasing cosmological constant which we interpret as an epoch of inflation followed by (pre-)heating when a rare event occurs in which the number of pixels increases by an order one fraction. The sudden appearance of radiation triggers an exponential increase in the number of pixels. Dark energy has a time varying equation of state with $w_a=-3惟_{m,0}(1+w_0)/2$, which is compatible with current bounds, and could be constrained further by future data releases. The pixelated nature of the Universe also implies a large-$l$ cutoff on the angular power spectrum of cosmological observables with $l_{\rm max} \sim O(N)$. We also use this pixel description to study the thermodynamics of de Sitter space, finding rough agreement with effective field theory considerations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1901.10489v1-abstract-full').style.display = 'none'; document.getElementById('1901.10489v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 January, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">62 pages, 7 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1811.01959">arXiv:1811.01959</a> <span> [<a href="https://arxiv.org/pdf/1811.01959">pdf</a>, <a href="https://arxiv.org/format/1811.01959">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/prop.201900057">10.1002/prop.201900057 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> F-theory and Dark Energy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Heckman%2C+J+J">Jonathan J. Heckman</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a>, <a href="/search/hep-th?searchtype=author&query=Zoccarato%2C+G">Gianluca Zoccarato</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1811.01959v3-abstract-short" style="display: inline;"> Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F-theory compactified on the warped product $\mathbb{R}_{\text{time}} \times S^3 \times Y_{8}$ where $Y_{8}$ is a $Spin(7)$ manifold, and the $S^3$ factor is the target space of an $SU(2)$ Wess--Zumino--Witten (WZW) model at level $N$. Reduction to M-theory exploits the abelian duality o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.01959v3-abstract-full').style.display = 'inline'; document.getElementById('1811.01959v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1811.01959v3-abstract-full" style="display: none;"> Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F-theory compactified on the warped product $\mathbb{R}_{\text{time}} \times S^3 \times Y_{8}$ where $Y_{8}$ is a $Spin(7)$ manifold, and the $S^3$ factor is the target space of an $SU(2)$ Wess--Zumino--Witten (WZW) model at level $N$. Reduction to M-theory exploits the abelian duality of this WZW model to an $S^3 / \mathbb{Z}_N$ orbifold. In the large $N$ limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7-branes in the $Spin(7)$ geometry is controlled by a Donaldson--Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as "$\mathcal{N} = 1/2$ supersymmetry" on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order $螖m_\text{4D} \sim \sqrt{M_\text{IR} M_\text{UV}}$ specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.01959v3-abstract-full').style.display = 'none'; document.getElementById('1811.01959v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 January, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3: 67 pages, 5 figures, reference added, typos corrected, revised analysis of superpartner masses</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1806.06066">arXiv:1806.06066</a> <span> [<a href="https://arxiv.org/pdf/1806.06066">pdf</a>, <a href="https://arxiv.org/format/1806.06066">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP10(2018)090">10.1007/JHEP10(2018)090 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Theories of Class F and Anomalies </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Martelli%2C+D">Dario Martelli</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1806.06066v3-abstract-short" style="display: inline;"> We consider the 6d (2,0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-dualit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.06066v3-abstract-full').style.display = 'inline'; document.getElementById('1806.06066v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1806.06066v3-abstract-full" style="display: none;"> We consider the 6d (2,0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-duality transformations. These monodromies occur around 2d loci in space-time, the duality defects, above which the fiber is singular. The key role that the fibration plays here motivates refering to this setup as theories of class F. In the simplest instance this gives rise to 4d N=4 Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z) monodromies. We determine the anomaly polynomial for these theories by pushing forward the anomaly polynomial of the 6d (2,0) theory along the fiber. This gives rise to corrections to the anomaly polynomials of 4d N=4 SYM and theories of class S. For the torus case, this analysis is complemented with a field theoretic derivation of a U(1) anomaly in 4d N=4 SYM. The corresponding anomaly polynomial is tested against known expressions of anomalies for wrapped D3-branes with varying coupling, which are known field theoretically and from holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories with varying coupling, are also discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.06066v3-abstract-full').style.display = 'none'; document.getElementById('1806.06066v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">54 pages, 1 figure, v2: added discussion of non-supersymmetric extension, v3: version as appears in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1709.07453">arXiv:1709.07453</a> <span> [<a href="https://arxiv.org/pdf/1709.07453">pdf</a>, <a href="https://arxiv.org/format/1709.07453">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP03(2018)069">10.1007/JHEP03(2018)069 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Baume%2C+F">Florent Baume</a>, <a href="/search/hep-th?searchtype=author&query=Cvetic%2C+M">Mirjam Cvetic</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Lin%2C+L">Ling Lin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1709.07453v1-abstract-short" style="display: inline;"> We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. To this end we consider complex structure deformations of elliptic fibrations with a Mordell--Weil group of rank one and identify the conditions under which the generating section becomes torsional. For the specific case of Z2 torsion we construct the generic solution to these conditions and show tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.07453v1-abstract-full').style.display = 'inline'; document.getElementById('1709.07453v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1709.07453v1-abstract-full" style="display: none;"> We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. To this end we consider complex structure deformations of elliptic fibrations with a Mordell--Weil group of rank one and identify the conditions under which the generating section becomes torsional. For the specific case of Z2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU(2) x SU(4)]/Z2 x SU(2). The subsolution with gauge group SU(2)/Z2 x SU(2), for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Z2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU(2)/Z2 x Z2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.07453v1-abstract-full').style.display = 'none'; document.getElementById('1709.07453v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 September, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">51 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UPR-1287-T </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.04679">arXiv:1705.04679</a> <span> [<a href="https://arxiv.org/pdf/1705.04679">pdf</a>, <a href="https://arxiv.org/ps/1705.04679">ps</a>, <a href="https://arxiv.org/format/1705.04679">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP08(2017)043">10.1007/JHEP08(2017)043 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> F-theory and AdS_3/CFT_2 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Couzens%2C+C">Christopher Couzens</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Martelli%2C+D">Dario Martelli</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Wong%2C+J">Jin-Mann Wong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.04679v2-abstract-short" style="display: inline;"> We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d N=(0,4) superconformal field theories with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the 6d N=(1,0) theory obta… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.04679v2-abstract-full').style.display = 'inline'; document.getElementById('1705.04679v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.04679v2-abstract-full" style="display: none;"> We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d N=(0,4) superconformal field theories with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the 6d N=(1,0) theory obtained from F-theory on Y_3. The non-trivial fibration over the wrapped curves implies a varying coupling of the N=4 Super-Yang-Mills theory on the D3-branes. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.04679v2-abstract-full').style.display = 'none'; document.getElementById('1705.04679v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">83 pages, v2: references added, typos corrected</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1612.06393">arXiv:1612.06393</a> <span> [<a href="https://arxiv.org/pdf/1612.06393">pdf</a>, <a href="https://arxiv.org/format/1612.06393">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP05(2017)103">10.1007/JHEP05(2017)103 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Gravitational Sector of 2d (0,2) F-theory Vacua </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Weigand%2C+T">Timo Weigand</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1612.06393v2-abstract-short" style="display: inline;"> F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.06393v2-abstract-full').style.display = 'inline'; document.getElementById('1612.06393v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1612.06393v2-abstract-full" style="display: none;"> F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S^1 reduction of the dual F-theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.06393v2-abstract-full').style.display = 'none'; document.getElementById('1612.06393v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 December, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, v2: JHEP version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1612.05640">arXiv:1612.05640</a> <span> [<a href="https://arxiv.org/pdf/1612.05640">pdf</a>, <a href="https://arxiv.org/format/1612.05640">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP04(2017)111">10.1007/JHEP04(2017)111 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Chiral 2d Theories from N=4 SYM with Varying Coupling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Weigand%2C+T">Timo Weigand</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1612.05640v3-abstract-short" style="display: inline;"> We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.05640v3-abstract-full').style.display = 'inline'; document.getElementById('1612.05640v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1612.05640v3-abstract-full" style="display: none;"> We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.05640v3-abstract-full').style.display = 'none'; document.getElementById('1612.05640v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 December, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">78 pages, 2 figures, v2: references added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1504.05593">arXiv:1504.05593</a> <span> [<a href="https://arxiv.org/pdf/1504.05593">pdf</a>, <a href="https://arxiv.org/format/1504.05593">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP09(2015)144">10.1007/JHEP09(2015)144 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a>, <a href="/search/hep-th?searchtype=author&query=Wong%2C+J">Jin-Mann Wong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1504.05593v2-abstract-short" style="display: inline;"> We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.05593v2-abstract-full').style.display = 'inline'; document.getElementById('1504.05593v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1504.05593v2-abstract-full" style="display: none;"> We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections. In view of modelling supersymmetric Grand Unified Theories, one of the main examples that we analyze are U(1) symmetries for SU(5) gauge theories with \bar{5} and 10 matter. We use a combination of constraints on the normal bundle of rational curves in Calabi-Yau three- and four-folds, as well as the splitting of rational curves in the fibers in codimension two, to determine the possible configurations of smooth rational sections. This analysis straightforwardly generalizes to multiple U(1)s. We study the flops of such fibers, as well as some of the Yukawa couplings in codimension three. Furthermore, we carry out a universal study of the U(1)-charged GUT singlets, including their KK-charges, and determine all realizations of singlet fibers. By giving vacuum expectation values to these singlets, we propose a systematic way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.05593v2-abstract-full').style.display = 'none'; document.getElementById('1504.05593v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">93 pages, 23 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> KCL-MTH-15-03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.4125">arXiv:1412.4125</a> <span> [<a href="https://arxiv.org/pdf/1412.4125">pdf</a>, <a href="https://arxiv.org/format/1412.4125">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP03(2015)055">10.1007/JHEP03(2015)055 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tate's Algorithm for F-theory GUTs with two U(1)s </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Sacco%2C+D">Damiano Sacco</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1412.4125v1-abstract-short" style="display: inline;"> We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) x U(1)^2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate's algorithm to elliptic fibrations with two U(1) symm… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.4125v1-abstract-full').style.display = 'inline'; document.getElementById('1412.4125v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.4125v1-abstract-full" style="display: none;"> We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) x U(1)^2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate's algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P^2. In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.4125v1-abstract-full').style.display = 'none'; document.getElementById('1412.4125v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">59 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> KCL-MTH-14-21 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.2653">arXiv:1402.2653</a> <span> [<a href="https://arxiv.org/pdf/1402.2653">pdf</a>, <a href="https://arxiv.org/format/1402.2653">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP05(2014)048">10.1007/JHEP05(2014)048 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Box Graphs and Singular Fibers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Hayashi%2C+H">Hirotaka Hayashi</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Morrison%2C+D+R">David R. Morrison</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1402.2653v2-abstract-short" style="display: inline;"> We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.2653v2-abstract-full').style.display = 'inline'; document.getElementById('1402.2653v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.2653v2-abstract-full" style="display: none;"> We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as `flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E_6, E_7 and E_8. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.2653v2-abstract-full').style.display = 'none'; document.getElementById('1402.2653v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">107 pages, 44 figures, v2: added case of E7 monodromy-reduced fibers</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IFT-UAM/CSIC-14-005, KCL-MTH-14-01, UCSB Math 2014-07 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.1678">arXiv:1304.1678</a> <span> [<a href="https://arxiv.org/pdf/1304.1678">pdf</a>, <a href="https://arxiv.org/ps/1304.1678">ps</a>, <a href="https://arxiv.org/format/1304.1678">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP10(2013)046">10.1007/JHEP10(2013)046 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Phases, Flops and F-theory: SU(5) Gauge Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Hayashi%2C+H">Hirotaka Hayashi</a>, <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.1678v2-abstract-short" style="display: inline;"> We consider F-theory and M-theory compactifications on singular Calabi-Yau fourfolds with an SU(5) singularity. On the M-theory side this realizes three-dimensional N=2 supersymmetric gauge theories with matter, and compactification on a resolution of the fourfold corresponds to passing to the Coulomb branch of the gauge theory. The classical phase structure of these theories has a simple characte… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1678v2-abstract-full').style.display = 'inline'; document.getElementById('1304.1678v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.1678v2-abstract-full" style="display: none;"> We consider F-theory and M-theory compactifications on singular Calabi-Yau fourfolds with an SU(5) singularity. On the M-theory side this realizes three-dimensional N=2 supersymmetric gauge theories with matter, and compactification on a resolution of the fourfold corresponds to passing to the Coulomb branch of the gauge theory. The classical phase structure of these theories has a simple characterization in terms of subwedges of the fundamental Weyl chamber of the gauge group. This phase structure has a counterpart in the network of small resolutions of the Calabi-Yau fourfold. We determine the geometric realization of each phase, which crucially depends on the fiber structure in codimension 2 and 3, including the network structure, which is realized in terms of flop transitions. This results in a set of small resolutions, which do not have a standard algebraic or toric realization, but are obtained by flops along codimension 2 (matter) loci. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1678v2-abstract-full').style.display = 'none'; document.getElementById('1304.1678v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 April, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">51 pages, v2: JHEP version, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> KCL-MTH-13-02, KIAS P-13017 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1212.2949">arXiv:1212.2949</a> <span> [<a href="https://arxiv.org/pdf/1212.2949">pdf</a>, <a href="https://arxiv.org/ps/1212.2949">ps</a>, <a href="https://arxiv.org/format/1212.2949">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP04(2013)061">10.1007/JHEP04(2013)061 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Tate Form on Steroids: Resolution and Higher Codimension Fibers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Lawrie%2C+C">Craig Lawrie</a>, <a href="/search/hep-th?searchtype=author&query=Schafer-Nameki%2C+S">Sakura Schafer-Nameki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1212.2949v2-abstract-short" style="display: inline;"> F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensional N=1 supersymmetric gauge theories, including matter and Yukawa couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1212.2949v2-abstract-full').style.display = 'inline'; document.getElementById('1212.2949v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1212.2949v2-abstract-full" style="display: none;"> F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensional N=1 supersymmetric gauge theories, including matter and Yukawa couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with an ADE type singularity in codimension 1 and study the structure of the fibers in codimension 2 and 3. We determine the fibers in higher codimension which in general are of Kodaira type along minimal singular loci, and are thus consistent with the low energy gauge-theoretic intuition. Furthermore, we provide a complementary description of the fibers in higher codimension, which will also be applicable to non-minimal singularities. The irreducible components in the fiber in codimension 2 correspond to weights of representations of the ADE gauge group. These can split further in codimension 3 in a way that is consistent with the generation of Yukawa couplings. Applying this reasoning, we then venture out to study non-minimal singularities, which occur for A type along codimension 3, and for D and E also in codimension 2. The fibers in this case are non-Kodaira, however some insight into these singularities can be gained by considering the splitting of fiber components along higher codimension, which are shown to be consistent with matter and Yukawa couplings for the corresponding gauge groups. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1212.2949v2-abstract-full').style.display = 'none'; document.getElementById('1212.2949v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 December, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">75 pages, v2: clarifications and references added, JHEP version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> KCL-MTH-12-14 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 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