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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/2411.14396">arXiv:2411.14396</a> <span> [<a href="https://arxiv.org/pdf/2411.14396">pdf</a>, <a href="https://arxiv.org/format/2411.14396">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Moore%2C+G+W">Gregory W. Moore</a>, <a href="/search/hep-th?searchtype=author&query=Saxena%2C+V">Vivek Saxena</a>, <a href="/search/hep-th?searchtype=author&query=Singh%2C+R+K">Ranveer Kumar Singh</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="2411.14396v1-abstract-short" style="display: inline;"> We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The exam… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.14396v1-abstract-full').style.display = 'inline'; document.getElementById('2411.14396v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.14396v1-abstract-full" style="display: none;"> We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The example of $\mathcal{N}=2^*$ theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional $\mathcal{N}=2$ theories and argue that the topological partition functions depend on (a): the diffeomorphism type of the spacetime, (b): the characteristic classes of background gerbe connections and (c): a "generalized spin-c structure," a concept we introduce and define. The main ideas are illustrated with both Lagrangian theories and class $\mathcal{S}$ theories. In the case of class $\mathcal{S}$ theories of $A_1$ type, we note that the different $S$-duality orbits of a theory associated with a fixed UV curve $C_{g,n}$ can have different topological data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.14396v1-abstract-full').style.display = 'none'; document.getElementById('2411.14396v1-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 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">46 pages + appendices = 97 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> YITP-SB-2024-22 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.19409">arXiv:2405.19409</a> <span> [<a href="https://arxiv.org/pdf/2405.19409">pdf</a>, <a href="https://arxiv.org/format/2405.19409">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</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(2024)056">10.1007/JHEP09(2024)056 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Saxena%2C+V">Vivek Saxena</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="2405.19409v3-abstract-short" style="display: inline;"> Motivated by recent developments connecting non-supersymmetric heterotic string theory to the theory of Topological Modular Forms (TMF), we show that the worldsheet theory with central charge $(17,\frac{3}{2})$ obtained by fibering the $(E_8)_1 \times (E_8)_1$ current algebra over the $\mathit{N}$=(0,1) sigma model on $S^{1}$ with antiperiodic spin structure (such that the two $E_8$ factors are ex… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.19409v3-abstract-full').style.display = 'inline'; document.getElementById('2405.19409v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.19409v3-abstract-full" style="display: none;"> Motivated by recent developments connecting non-supersymmetric heterotic string theory to the theory of Topological Modular Forms (TMF), we show that the worldsheet theory with central charge $(17,\frac{3}{2})$ obtained by fibering the $(E_8)_1 \times (E_8)_1$ current algebra over the $\mathit{N}$=(0,1) sigma model on $S^{1}$ with antiperiodic spin structure (such that the two $E_8$ factors are exchanged as we go around the circle), is continuously connected to the $(E_8)_2$ theory in the Gaiotto$-$Johnson-Freyd$-$Witten sense of going "up and down the RG trajectories". Combined with the work of Tachikawa and Yamashita, this furnishes a physical derivation of the fact that the $(E_8)_2$ theory corresponds to the unique nontrivial torsion element $[(E_8)_2]$ of $\mathsf{TMF}^{31}$ with zero mod-2 elliptic genus. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.19409v3-abstract-full').style.display = 'none'; document.getElementById('2405.19409v3-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 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">26 pages + appendices; References updated; Content matches published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2024, 56 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.08394">arXiv:2311.08394</a> <span> [<a href="https://arxiv.org/pdf/2311.08394">pdf</a>, <a href="https://arxiv.org/format/2311.08394">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Superconformal Gravity And The Topology Of Diffeomorphism Groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Cushing%2C+J">Jay Cushing</a>, <a href="/search/hep-th?searchtype=author&query=Moore%2C+G+W">Gregory W. Moore</a>, <a href="/search/hep-th?searchtype=author&query=Ro%C4%8Dek%2C+M">Martin Ro膷ek</a>, <a href="/search/hep-th?searchtype=author&query=Saxena%2C+V">Vivek Saxena</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="2311.08394v2-abstract-short" style="display: inline;"> Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a useful point of view on the Donaldson and Seiberg-Witten invariants of four-manifolds. In this paper we generalize the construction to include a path integral formulation of generalizations of Donaldson invariants for smooth families of four-manifolds. Mathematically these are equivariant cohomology classes for the action o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.08394v2-abstract-full').style.display = 'inline'; document.getElementById('2311.08394v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.08394v2-abstract-full" style="display: none;"> Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a useful point of view on the Donaldson and Seiberg-Witten invariants of four-manifolds. In this paper we generalize the construction to include a path integral formulation of generalizations of Donaldson invariants for smooth families of four-manifolds. Mathematically these are equivariant cohomology classes for the action of the oriented diffeomorphism group on the space of metrics on the manifold. In principle these cohomology classes should contain nontrivial information about the topology of the diffeomorphism group of the four-manifold. We show that the invariants may be interpreted as the standard topologically twisted path integral of four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills coupled to topologically twisted background fields of conformal supergravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.08394v2-abstract-full').style.display = 'none'; document.getElementById('2311.08394v2-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> 17 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">79 pages + appendices = 166 pages; 1 figure; Hyperlinks fixed</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> YITP-SB-2023-32 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.09574">arXiv:1911.09574</a> <span> [<a href="https://arxiv.org/pdf/1911.09574">pdf</a>, <a href="https://arxiv.org/format/1911.09574">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(2020)198">10.1007/JHEP04(2020)198 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Saxena%2C+V">Vivek Saxena</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="1911.09574v3-abstract-short" style="display: inline;"> We carry out a detailed exploration of the deformations of rank-two five-dimensional superconformal field theories (SCFTs) $\mathcal{T}_{\mathbf{X}}$, which are geometrically engineered by M-theory on the space transverse to isolated toric Calabi-Yau (CY) threefold singularities $\mathbf{X}$. Deformations of 5d $\mathcal{N}=1$ SCFTs can lead to "gauge-theory phases," but also to "non-gauge-theoret… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.09574v3-abstract-full').style.display = 'inline'; document.getElementById('1911.09574v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.09574v3-abstract-full" style="display: none;"> We carry out a detailed exploration of the deformations of rank-two five-dimensional superconformal field theories (SCFTs) $\mathcal{T}_{\mathbf{X}}$, which are geometrically engineered by M-theory on the space transverse to isolated toric Calabi-Yau (CY) threefold singularities $\mathbf{X}$. Deformations of 5d $\mathcal{N}=1$ SCFTs can lead to "gauge-theory phases," but also to "non-gauge-theoretic phases," which have no known Lagrangian interpretation. In previous work, a technique relying on fiberwise M-theory/type IIA duality was developed to associate a type IIA background to any resolution of $\mathbf{X}$ which admits a suitable projection of its toric diagram. The type IIA background consists of an A-type ALE space fibered over the real line, with stacks of coincident D6-branes wrapping 2-cycles in the ALE resolution. In this work, we combine that technique with some elementary ideas from graph theory, to analyze mass deformations of $\mathcal{T}_{\mathbf{X}}$ when $\mathbf{X}$ is a isolated toric CY$_3$ singularity of rank-two (that is, it has two compact divisors). We explicitly derive type IIA descriptions of all isolated rank-two CY$_3$ toric singularities. We also comment on the renormalization group flows in the extended parameter spaces of these theories, which frequently relate distinct geometries by flowing to theories with lower flavor symmetries, including those that describe non-gauge-theoretic phases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.09574v3-abstract-full').style.display = 'none'; document.getElementById('1911.09574v3-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 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">73 pages + appendices (92 pp.); many figures. Added comments. Content matches the JHEP version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> YITP-SB-19-41 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2020, 198 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.10451">arXiv:1812.10451</a> <span> [<a href="https://arxiv.org/pdf/1812.10451">pdf</a>, <a href="https://arxiv.org/format/1812.10451">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/10.21468/SciPostPhys.6.5.052">10.21468/SciPostPhys.6.5.052 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Closset%2C+C">Cyril Closset</a>, <a href="/search/hep-th?searchtype=author&query=Del+Zotto%2C+M">Michele Del Zotto</a>, <a href="/search/hep-th?searchtype=author&query=Saxena%2C+V">Vivek Saxena</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="1812.10451v3-abstract-short" style="display: inline;"> We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.10451v3-abstract-full').style.display = 'inline'; document.getElementById('1812.10451v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.10451v3-abstract-full" style="display: none;"> We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$ fibered over a real line, and the map between the K盲hler parameters of $\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA "reductions" give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d $\mathcal{N}=1$ gauge theories. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.10451v3-abstract-full').style.display = 'none'; document.getElementById('1812.10451v3-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> 17 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">89 pages plus appendix, many figures; v2: corrected typos and added references; added comment in sec.4.3, SciPost version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> YITP-SB-18-41 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SciPost Phys. 6, 052 (2019) </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 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