exotic brane in nLab

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title> exotic brane in nLab </title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <meta name="robots" content="noindex,nofollow" /> <style type="text/css"> h1#pageName, div.info, .newWikiWord a, a.existingWikiWord, .newWikiWord a:hover, [actiontype="toggle"]:hover, #TextileHelp h3 { color: #226622; } </style> <link href="/stylesheets/instiki.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <style type="text/css"><![CDATA[/*></style> <script src="/javascripts/prototype.js?1660229990" type="text/javascript"></script> <script src="/javascripts/effects.js?1660229990" type="text/javascript"></script> <script src="/javascripts/dragdrop.js?1660229990" type="text/javascript"></script> <script src="/javascripts/controls.js?1660229990" type="text/javascript"></script> <script src="/javascripts/application.js?1660229990" type="text/javascript"></script> <script type="text/javascript"> <![CDATA[//><!]]> </script> </head> <body> <div id="Container"> <textarea id='content' readonly=' readonly' rows='24' cols='60' >[[!redirects Exotic branes]] +-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### String theory +-- {: .hide} [[!include string theory - contents]] =-- #### Duality +--{: .hide} [[!include duality - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea In [[string theory]], by "exotic branes" &lbrack;[deBoer & Shigemori (2012)](#deBoerShigemori12)&rbrack; one means first of all $p$-[[branes]] of small [[codimension]] $D-1-p \leq 2$ ("non-standard branes" [Bergshoeff & Riccioni (2012](#BergshoeffRiccioni12))), such as * [[D7-branes]] (codimension 2 [[defect branes]]), * [[D8-branes]] and maybe [[M9-branes]] (codimension 1) * [[D9-branes]] (codimension 0). More generally, exotic branes have been argued to be [[U-duality]]-twisted objects in [[non-geometric backgrounds]]. According to [deBoer & Shigemori 2012, p. 12](#deBoerShigemori12) all these may be identified as [[codimension]]-2 [[defect branes]] with [[U-duality]]-[[group]] [[monodromy]]. \begin{imagefromfile} "file_name": "exotic_branes.jpg", "web": "nlab", "width": 800, "height": 475, "unit": "px", "alt": "exotic branes" \end{imagefromfile} >Figure 1 from ([BMO19](#BMO19)). <<A comparison of the objects covered by the geometric solutions (backed by orange hashing) and [[non-geometric solutions]] (backed by green hashing) out of all the [[branes]] down to codimension-$2$ and[^1] $0\leq\alpha\leq -2$, as well as their [[M-theory]] lifts. Red lines denote [[T-duality]], blue lines denote lifts/[[double dimensional reduction|reductions]] and black lines denote [[S-dualities]].>> [^1]: Here $\alpha$ denotes the [[exponent]] with which the brane's [[tension]] $T$ scales with the [[string coupling constant]] $g_s$ as $T \propto (g_s)^\alpha$, according to [BMO 2019](#BMO19), [p. 2](https://arxiv.org/pdf/1903.10247.pdf#page=2). ## Related concepts * [[non-geometry]], [[T-fold]] * [[double field theory]] * [[defect brane]] ## References Branes of [[codimension]] $\leq 2$ are called *non-standard branes* in: * {#BergshoeffRiccioni12} [[Eric A. Bergshoeff]], [[Fabio Riccioni]], *Solitonic branes and wrapping rules*, Phys. Part. Nuclei **43** (2012) 557–561 &lbrack;[doi:10.1134/S106377961205005X](https://doi.org/10.1134/S106377961205005X)&rbrack; > (see also at *[[solitonic brane]]*) The terminology "exotic branes" is due to: * {#deBoerShigemori12} [[Jan de Boer]], [[Masaki Shigemori]], _Exotic Branes in String Theory_, Physics Reports **532** (2013) 65-118 ([arXiv:1209.6056](https://arxiv.org/abs/1209.6056), [doi:j.physrep.2013.07.003](https://doi.org/10.1016/j.physrep.2013.07.003)) > (discussion as [[defect branes]] with [[U-duality]]-[[group]] [[monodromy]]) * [[David Berman]], Felix J. Rudolph, _Branes are Waves and Monopoles_ &lbrack;[arXiv:1409.6314](https://arxiv.org/abs/1409.6314)&rbrack; * [[Jose J. Fernandez-Melgarejo]], [[Tetsuji Kimura]], [[Yuho Sakatani]], *Weaving the Exotic Web*, JHEP **2018** 72 (2018) &lbrack;<a href="https://doi.org/10.1007/JHEP09(2018)072">doi:10.1007/JHEP09(2018)072</a>&rbrack; * {#BermanMusaevOtsuki18} [[David S. Berman]], [[Edvard T. Musaev]], [[Ray Otsuki]], *Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond*, J. High Energ. Phys. **2018** 53 (2018) &lbrack;[arXiv:1806.00430v4](https://arxiv.org/abs/1806.00430), <a href="https://doi.org/10.1007/JHEP12(2018)053">doi:10.1007/JHEP12(2018)053</a>&rbrack; * {#BMO19} [[David Berman]], [[Edvard Musaev]], [[Ray Otsuki]], _Exotic Branes in M-Theory_, contribution to: *[Dualities and Generalized Geometries, Corfu Summer Institute 2018](http://www.physics.ntua.gr/corfu2018/dg.html)* ([arXiv:1903.10247](https://arxiv.org/abs/1903.10247)) [[!redirects exotic branes]] [[!redirects Exotic branes]] [[!redirects Exotic brane]] [[!redirects non-geometric branes]] [[!redirects non-geometric brane]]</textarea> </div>  </body> </html>

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exotic brane in nLab