CINXE.COM
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="index,follow" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <link href="/stylesheets/instiki.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/mathematics.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/syntax.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/nlab.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/gh/dreampulse/computer-modern-web-font@master/fonts.css"/> <style type="text/css"> h1#pageName, div.info, .newWikiWord a, a.existingWikiWord, .newWikiWord a:hover, [actiontype="toggle"]:hover, #TextileHelp h3 { color: #226622; } a:visited.existingWikiWord { color: #164416; } </style> <style type="text/css"><!--/*--><![CDATA[/*><!--*/ .toc ul {margin: 0; padding: 0;} .toc ul ul {margin: 0; padding: 0 0 0 10px;} .toc li > p {margin: 0} .toc ul li {list-style-type: none; position: relative;} .toc div {border-top:1px dotted #ccc;} .rightHandSide h2 {font-size: 1.5em;color:#008B26} table.plaintable { border-collapse:collapse; margin-left:30px; border:0; } .plaintable td {border:1px solid #000; padding: 3px;} .plaintable th {padding: 3px;} .plaintable caption { font-weight: bold; font-size:1.1em; text-align:center; margin-left:30px; } /* Query boxes for questioning and answering mechanism */ div.query{ background: #f6fff3; border: solid #ce9; border-width: 2px 1px; padding: 0 1em; margin: 0 1em; max-height: 20em; overflow: auto; } /* Standout boxes for putting important text */ div.standout{ background: #fff1f1; border: solid black; border-width: 2px 1px; padding: 0 1em; margin: 0 1em; overflow: auto; } /* Icon for links to n-category arXiv documents (commented out for now i.e. disabled) a[href*="http://arxiv.org/"] { background-image: url(../files/arXiv_icon.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 22px; } */ /* Icon for links to n-category cafe posts (disabled) a[href*="http://golem.ph.utexas.edu/category"] { background-image: url(../files/n-cafe_5.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ /* Icon for links to pdf files (disabled) a[href$=".pdf"] { background-image: url(../files/pdficon_small.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ /* Icon for links to pages, etc. -inside- pdf files (disabled) a[href*=".pdf#"] { background-image: url(../files/pdf_entry.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ a.existingWikiWord { color: #226622; } a.existingWikiWord:visited { color: #226622; } a.existingWikiWord[title] { border: 0px; color: #aa0505; text-decoration: none; } a.existingWikiWord[title]:visited { border: 0px; color: #551111; text-decoration: none; } a[href^="http://"] { border: 0px; color: #003399; } a[href^="http://"]:visited { border: 0px; color: #330066; } a[href^="https://"] { border: 0px; color: #003399; } a[href^="https://"]:visited { border: 0px; color: #330066; } div.dropDown .hide { display: none; } div.dropDown:hover .hide { display:block; } div.clickDown .hide { display: none; } div.clickDown:focus { outline:none; } div.clickDown:focus .hide, div.clickDown:hover .hide { display: block; } div.clickDown .clickToReveal, div.clickDown:focus .clickToHide { display:block; } div.clickDown:focus .clickToReveal, div.clickDown .clickToHide { display:none; } div.clickDown .clickToReveal:after { content: "A(Hover to reveal, click to "hold")"; font-size: 60%; } div.clickDown .clickToHide:after { content: "A(Click to hide)"; font-size: 60%; } div.clickDown .clickToHide, div.clickDown .clickToReveal { white-space: pre-wrap; } .un_theorem, .num_theorem, .un_lemma, .num_lemma, .un_prop, .num_prop, .un_cor, .num_cor, .un_defn, .num_defn, .un_example, .num_example, .un_note, .num_note, .un_remark, .num_remark { margin-left: 1em; } span.theorem_label { margin-left: -1em; } .proof span.theorem_label { margin-left: 0em; } :target { background-color: #BBBBBB; border-radius: 5pt; } /*]]>*/--></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 src="/javascripts/page_helper.js?1660229990" type="text/javascript"></script> <script src="/javascripts/thm_numbering.js?1660229990" type="text/javascript"></script> <script type="text/x-mathjax-config"> <!--//--><![CDATA[//><!-- MathJax.Ajax.config.path["Contrib"] = "/MathJax"; MathJax.Hub.Config({ MathML: { useMathMLspacing: true }, "HTML-CSS": { scale: 90, extensions: ["handle-floats.js"] } }); MathJax.Hub.Queue( function () { var fos = document.getElementsByTagName('foreignObject'); for (var i = 0; i < fos.length; i++) { MathJax.Hub.Typeset(fos[i]); } }); //--><!]]> </script> <script type="text/javascript"> <!--//--><![CDATA[//><!-- window.addEventListener("DOMContentLoaded", function () { var div = document.createElement('div'); var math = document.createElementNS('http://www.w3.org/1998/Math/MathML', 'math'); document.body.appendChild(div); div.appendChild(math); // Test for MathML support comparable to WebKit version https://trac.webkit.org/changeset/203640 or higher. div.setAttribute('style', 'font-style: italic'); var mathml_unsupported = !(window.getComputedStyle(div.firstChild).getPropertyValue('font-style') === 'normal'); div.parentNode.removeChild(div); if (mathml_unsupported) { // MathML does not seem to be supported... var s = document.createElement('script'); s.src = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=MML_HTMLorMML-full"; document.querySelector('head').appendChild(s); } else { document.head.insertAdjacentHTML("beforeend", '<style>svg[viewBox] {max-width: 100%}</style>'); } }); //--><!]]> </script> <link href="https://ncatlab.org/nlab/atom_with_headlines" rel="alternate" title="Atom with headlines" type="application/atom+xml" /> <link href="https://ncatlab.org/nlab/atom_with_content" rel="alternate" title="Atom with full content" type="application/atom+xml" /> <script type="text/javascript"> document.observe("dom:loaded", function() { generateThmNumbers(); }); </script> </head> <body> <div id="Container"> <div id="Content"> <h1 id="pageName"> <span style="float: left; margin: 0.5em 0.25em -0.25em 0"> <svg xmlns="http://www.w3.org/2000/svg" width="1.872em" height="1.8em" viewBox="0 0 190 181"> <path fill="#226622" d="M72.8 145c-1.6 17.3-15.7 10-23.6 20.2-5.6 7.3 4.8 15 11.4 15 11.5-.2 19-13.4 26.4-20.3 3.3-3 8.2-4 11.2-7.2a14 14 0 0 0 2.9-11.1c-1.4-9.6-12.4-18.6-16.9-27.2-5-9.6-10.7-27.4-24.1-27.7-17.4-.3-.4 26 4.7 30.7 2.4 2.3 5.4 4.1 7.3 6.9 1.6 2.3 2.1 5.8-1 7.2-5.9 2.6-12.4-6.3-15.5-10-8.8-10.6-15.5-23-26.2-31.8-5.2-4.3-11.8-8-18-3.7-7.3 4.9-4.2 12.9.2 18.5a81 81 0 0 0 30.7 23c3.3 1.5 12.8 5.6 10 10.7-2.5 5.2-11.7 3-15.6 1.1-8.4-3.8-24.3-21.3-34.4-13.7-3.5 2.6-2.3 7.6-1.2 11.1 2.8 9 12.2 17.2 20.9 20.5 17.3 6.7 34.3-8 50.8-12.1z"/> <path fill="#a41e32" d="M145.9 121.3c-.2-7.5 0-19.6-4.5-26-5.4-7.5-12.9-1-14.1 5.8-1.4 7.8 2.7 14.1 4.8 21.3 3.4 12 5.8 29-.8 40.1-3.6-6.7-5.2-13-7-20.4-2.1-8.2-12.8-13.2-15.1-1.9-2 9.7 9 21.2 12 30.1 1.2 4 2 8.8 6.4 10.3 6.9 2.3 13.3-4.7 17.7-8.8 12.2-11.5 36.6-20.7 43.4-36.4 6.7-15.7-13.7-14-21.3-7.2-9.1 8-11.9 20.5-23.6 25.1 7.5-23.7 31.8-37.6 38.4-61.4 2-7.3-.8-29.6-13-19.8-14.5 11.6-6.6 37.6-23.3 49.2z"/> <path fill="#193c78" d="M86.3 47.5c0-13-10.2-27.6-5.8-40.4 2.8-8.4 14.1-10.1 17-1 3.8 11.6-.3 26.3-1.8 38 11.7-.7 10.5-16 14.8-24.3 2.1-4.2 5.7-9.1 11-6.7 6 2.7 7.4 9.2 6.6 15.1-2.2 14-12.2 18.8-22.4 27-3.4 2.7-8 6.6-5.9 11.6 2 4.4 7 4.5 10.7 2.8 7.4-3.3 13.4-16.5 21.7-16 14.6.7 12 21.9.9 26.2-5 1.9-10.2 2.3-15.2 3.9-5.8 1.8-9.4 8.7-15.7 8.9-6.1.1-9-6.9-14.3-9-14.4-6-33.3-2-44.7-14.7-3.7-4.2-9.6-12-4.9-17.4 9.3-10.7 28 7.2 35.7 12 2 1.1 11 6.9 11.4 1.1.4-5.2-10-8.2-13.5-10-11.1-5.2-30-15.3-35-27.3-2.5-6 2.8-13.8 9.4-13.6 6.9.2 13.4 7 17.5 12C70.9 34 75 43.8 86.3 47.4z"/> </svg> </span> <span class="webName">nLab</span> exotic brane </h1> <div class="navigation"> <span class="skipNav"><a href='#navEnd'>Skip the Navigation Links</a> | </span> <span style="display:inline-block; width: 0.3em;"></span> <a href="/nlab/show/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/11256/#Item_9" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <div class="rightHandSide"> <div class="toc clickDown" tabindex="0"> <h3 id="context">Context</h3> <h4 id="string_theory">String theory</h4> <div class="hide"><div> <ul> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a></strong></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/books+about+string+theory">books about string theory</a></p> </li> </ul> <h3 id="ingredients">Ingredients</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a>,</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/CFT">CFT</a>, <a class="existingWikiWord" href="/nlab/show/perturbation+theory">perturbation theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/effective+QFT">effective background QFT</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/gravity">gravity</a>, <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, <a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a>, <a class="existingWikiWord" href="/nlab/show/quantum+gravity">quantum gravity</a></li> </ul> </li> </ul> <h3 id="critical_string_models">Critical string models</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/heterotic+string+theory">heterotic string theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Green-Schwarz+mechanism">Green-Schwarz mechanism</a>, <a class="existingWikiWord" href="/nlab/show/differential+string+structure">differential string structure</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/dual+heterotic+string+theory">dual heterotic string theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/differential+fivebrane+structure">differential fivebrane structure</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/type+II+string+theory">type II string theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/type+IIA+string+theory">type IIA string theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/type+IIB+string+theory">type IIB string theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/F-theory">F-theory</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+field+theory">string field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/duality+in+string+theory">duality in string theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/T-duality">T-duality</a>, <a class="existingWikiWord" href="/nlab/show/mirror+symmetry">mirror symmetry</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/S-duality">S-duality</a>, <a class="existingWikiWord" href="/nlab/show/electric-magnetic+duality">electric-magnetic duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/open%2Fclosed+string+duality">open/closed string duality</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/AdS%2FCFT+correspondence">AdS/CFT correspondence</a>, <a class="existingWikiWord" href="/nlab/show/holographic+principle">holographic principle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></p> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/11-dimensional+supergravity">11-dimensional supergravity</a>, <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Ho%C5%99ava-Witten+theory">Hořava-Witten theory</a></li> </ul> </li> </ul> <h3 id="extended_objects">Extended objects</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/brane">brane</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/D-brane">D-brane</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/D0-brane">D0-brane</a>, <a class="existingWikiWord" href="/nlab/show/D2-brane">D2-brane</a>, <a class="existingWikiWord" href="/nlab/show/D4-brane">D4-brane</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/D1-brane">D1-brane</a>, <a class="existingWikiWord" href="/nlab/show/D3-brane">D3-brane</a>, <a class="existingWikiWord" href="/nlab/show/D5-brane">D5-brane</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/RR-field">RR-field</a>, <a class="existingWikiWord" href="/nlab/show/differential+K-theory">differential K-theory</a></p> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/NS-brane">NS-brane</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/string">string</a>, <a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/spinning+string">spinning string</a>, <a class="existingWikiWord" href="/nlab/show/superstring">superstring</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/B2-field">B2-field</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/NS5-brane">NS5-brane</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/B6-field">B6-field</a></li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/M-brane">M-brane</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/C3-field">C3-field</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/ABJM+theory">ABJM theory</a>, <a class="existingWikiWord" href="/nlab/show/BLG+model">BLG model</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/M5-brane">M5-brane</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/C6-field">C6-field</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-supersymmetric+QFT">6d (2,0)-supersymmetric QFT</a></p> </li> </ul> </li> </ul> </li> </ul> <h3 id="topological_strings">Topological strings</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+string">topological string</a>, <a class="existingWikiWord" href="/nlab/show/TCFT">TCFT</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/A-model">A-model</a>, <a class="existingWikiWord" href="/nlab/show/B-model">B-model</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+M-theory">topological M-theory</a></p> </li> </ul> <h2 id="backgrounds">Backgrounds</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/target+space">target space</a>, <a class="existingWikiWord" href="/nlab/show/background+gauge+field">background gauge field</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/twisted+smooth+cohomology+in+string+theory">twisted smooth cohomology in string theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/landscape+of+string+theory+vacua">landscape of string theory vacua</a></p> </li> </ul> <h2 id="phenomenology">Phenomenology</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/string+phenomenology">string phenomenology</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/moduli+stabilization">moduli stabilization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/G%E2%82%82-MSSM">G₂-MSSM</a></p> </li> </ul> </li> </ul> <div> <p> <a href="/nlab/edit/string+theory+-+contents">Edit this sidebar</a> </p> </div></div></div> <h4 id="duality">Duality</h4> <div class="hide"><div> <p><strong><a class="existingWikiWord" href="/nlab/show/duality">duality</a></strong></p> <ul> <li> <p>abstract duality: <a class="existingWikiWord" href="/nlab/show/opposite+category">opposite category</a>,</p> <p><a class="existingWikiWord" href="/nlab/show/Eckmann-Hilton+duality">Eckmann-Hilton duality</a></p> </li> <li> <p>concrete duality: <a class="existingWikiWord" href="/nlab/show/dual+object">dual object</a>, <a class="existingWikiWord" href="/nlab/show/dualizable+object">dualizable object</a>, <a class="existingWikiWord" href="/nlab/show/fully+dualizable+object">fully dualizable object</a>, <a class="existingWikiWord" href="/nlab/show/dualizing+object">dualizing object</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/dual+vector+space">dual vector space</a></li> </ul> </li> </ul> <p><strong>Examples</strong></p> <ul> <li> <p>between <a class="existingWikiWord" href="/nlab/show/higher+geometry">higher geometry</a>/<a class="existingWikiWord" href="/nlab/show/higher+algebra">higher algebra</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Isbell+duality">Isbell duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Stone+duality">Stone duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Gelfand+duality">Gelfand duality</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Tannaka+duality">Tannaka duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Langlands+duality">Langlands duality</a>, <a class="existingWikiWord" href="/nlab/show/geometric+Langlands+duality">geometric Langlands duality</a>, <a class="existingWikiWord" href="/nlab/show/quantum+geometric+Langlands+duality">quantum geometric Langlands duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Pontryagin+duality">Pontryagin duality</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Cartier+duality">Cartier duality</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Poincar%C3%A9+duality">Poincaré duality</a> for <a class="existingWikiWord" href="/nlab/show/manifolds">manifolds</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Koszul+duality">Koszul duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Spanier-Whitehead+duality">Spanier-Whitehead duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Grothendieck+duality">Grothendieck duality</a></p> </li> </ul> <p><strong>In QFT and String theory</strong></p> <p><strong><a class="existingWikiWord" href="/nlab/show/duality+in+physics">duality in physics</a></strong>, <strong><a class="existingWikiWord" href="/nlab/show/duality+in+string+theory">duality in string theory</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Seiberg+duality">Seiberg duality</a>, <a class="existingWikiWord" href="/nlab/show/AGT+conjecture">AGT conjecture</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/S-duality">S-duality</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/electro-magnetic+duality">electro-magnetic duality</a>, <a class="existingWikiWord" href="/nlab/show/Montonen-Olive+duality">Montonen-Olive duality</a>, <a class="existingWikiWord" href="/nlab/show/geometric+Langlands+duality">geometric Langlands duality</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/T-duality">T-duality</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/mirror+symmetry">mirror symmetry</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/open%2Fclosed+string+duality">open/closed string duality</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/AdS%2FCFT">AdS/CFT duality</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></p> </li> </ul> </li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#references'>References</a></li> </ul> </div> <h2 id="idea">Idea</h2> <p>In <a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a>, by “exotic branes” [<a href="#deBoerShigemori12">deBoer & Shigemori (2012)</a>] one means first of all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math>-<a class="existingWikiWord" href="/nlab/show/branes">branes</a> of small <a class="existingWikiWord" href="/nlab/show/codimension">codimension</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>D</mi><mo>−</mo><mn>1</mn><mo>−</mo><mi>p</mi><mo>≤</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">D-1-p \leq 2</annotation></semantics></math> (“non-standard branes” <a href="#BergshoeffRiccioni12">Bergshoeff & Riccioni (2012</a>)), such as</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/D7-branes">D7-branes</a> (codimension 2 <a class="existingWikiWord" href="/nlab/show/defect+branes">defect branes</a>),</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/D8-branes">D8-branes</a> and maybe <a class="existingWikiWord" href="/nlab/show/M9-branes">M9-branes</a> (codimension 1)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/D9-branes">D9-branes</a> (codimension 0).</p> </li> </ul> <p>More generally, exotic branes have been argued to be <a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a>-twisted objects in <a class="existingWikiWord" href="/nlab/show/non-geometric+backgrounds">non-geometric backgrounds</a>.</p> <p>According to <a href="#deBoerShigemori12">deBoer & Shigemori 2012, p. 12</a> all these may be identified as <a class="existingWikiWord" href="/nlab/show/codimension">codimension</a>-2 <a class="existingWikiWord" href="/nlab/show/defect+branes">defect branes</a> with <a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a>-<a class="existingWikiWord" href="/nlab/show/group">group</a> <a class="existingWikiWord" href="/nlab/show/monodromy">monodromy</a>.</p> <p><img src="/nlab/files/exotic_branes.jpg" width="800px" height="475px" alt="exotic branes" /></p> <blockquote> <p>Figure 1 from (<a href="#BMO19">BMO19</a>). «A comparison of the objects covered by the geometric solutions (backed by orange hashing) and <a class="existingWikiWord" href="/nlab/show/non-geometric+solutions">non-geometric solutions</a> (backed by green hashing) out of all the <a class="existingWikiWord" href="/nlab/show/branes">branes</a> down to codimension-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math> and<sup id="fnref:1"><a href="#fn:1" rel="footnote">1</a></sup> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mo lspace="verythinmathspace" rspace="0em">−</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">0\leq\alpha\leq -2</annotation></semantics></math>, as well as their <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a> lifts. Red lines denote <a class="existingWikiWord" href="/nlab/show/T-duality">T-duality</a>, blue lines denote lifts/<a class="existingWikiWord" href="/nlab/show/double+dimensional+reduction">reductions</a> and black lines denote <a class="existingWikiWord" href="/nlab/show/S-dualities">S-dualities</a>.»</p> </blockquote> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/non-geometry">non-geometry</a>, <a class="existingWikiWord" href="/nlab/show/T-fold">T-fold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/double+field+theory">double field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/defect+brane">defect brane</a></p> </li> </ul> <h2 id="references">References</h2> <p>Branes of <a class="existingWikiWord" href="/nlab/show/codimension">codimension</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo>≤</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\leq 2</annotation></semantics></math> are called <em>non-standard branes</em> in:</p> <ul> <li id="BergshoeffRiccioni12"> <p><a class="existingWikiWord" href="/nlab/show/Eric+A.+Bergshoeff">Eric A. Bergshoeff</a>, <a class="existingWikiWord" href="/nlab/show/Fabio+Riccioni">Fabio Riccioni</a>, <em>Solitonic branes and wrapping rules</em>, Phys. Part. Nuclei <strong>43</strong> (2012) 557–561 [<a href="https://doi.org/10.1134/S106377961205005X">doi:10.1134/S106377961205005X</a>]</p> <blockquote> <p>(see also at <em><a class="existingWikiWord" href="/nlab/show/solitonic+brane">solitonic brane</a></em>)</p> </blockquote> </li> </ul> <p>The terminology “exotic branes” is due to:</p> <ul> <li id="deBoerShigemori12"> <p><a class="existingWikiWord" href="/nlab/show/Jan+de+Boer">Jan de Boer</a>, <a class="existingWikiWord" href="/nlab/show/Masaki+Shigemori">Masaki Shigemori</a>, <em>Exotic Branes in String Theory</em>, Physics Reports <strong>532</strong> (2013) 65-118 (<a href="https://arxiv.org/abs/1209.6056">arXiv:1209.6056</a>, <a href="https://doi.org/10.1016/j.physrep.2013.07.003">doi:j.physrep.2013.07.003</a>)</p> <blockquote> <p>(discussion as <a class="existingWikiWord" href="/nlab/show/defect+branes">defect branes</a> with <a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a>-<a class="existingWikiWord" href="/nlab/show/group">group</a> <a class="existingWikiWord" href="/nlab/show/monodromy">monodromy</a>)</p> </blockquote> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/David+Berman">David Berman</a>, Felix J. Rudolph, <em>Branes are Waves and Monopoles</em> [<a href="https://arxiv.org/abs/1409.6314">arXiv:1409.6314</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Jose+J.+Fernandez-Melgarejo">Jose J. Fernandez-Melgarejo</a>, <a class="existingWikiWord" href="/nlab/show/Tetsuji+Kimura">Tetsuji Kimura</a>, <a class="existingWikiWord" href="/nlab/show/Yuho+Sakatani">Yuho Sakatani</a>, <em>Weaving the Exotic Web</em>, JHEP <strong>2018</strong> 72 (2018) [<a href="https://doi.org/10.1007/JHEP09(2018)072">doi:10.1007/JHEP09(2018)072</a>]</p> </li> <li id="BermanMusaevOtsuki18"> <p><a class="existingWikiWord" href="/nlab/show/David+S.+Berman">David S. Berman</a>, <a class="existingWikiWord" href="/nlab/show/Edvard+T.+Musaev">Edvard T. Musaev</a>, <a class="existingWikiWord" href="/nlab/show/Ray+Otsuki">Ray Otsuki</a>, <em>Exotic Branes in Exceptional Field Theory: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>E</mi> <mrow><mn>7</mn><mo stretchy="false">(</mo><mn>7</mn><mo stretchy="false">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">E_{7(7)}</annotation></semantics></math> and Beyond</em>, J. High Energ. Phys. <strong>2018</strong> 53 (2018) [<a href="https://arxiv.org/abs/1806.00430">arXiv:1806.00430v4</a>, <a href="https://doi.org/10.1007/JHEP12(2018)053">doi:10.1007/JHEP12(2018)053</a>]</p> </li> <li id="BMO19"> <p><a class="existingWikiWord" href="/nlab/show/David+Berman">David Berman</a>, <a class="existingWikiWord" href="/nlab/show/Edvard+Musaev">Edvard Musaev</a>, <a class="existingWikiWord" href="/nlab/show/Ray+Otsuki">Ray Otsuki</a>, <em>Exotic Branes in M-Theory</em>, contribution to: <em><a href="http://www.physics.ntua.gr/corfu2018/dg.html">Dualities and Generalized Geometries, Corfu Summer Institute 2018</a></em> (<a href="https://arxiv.org/abs/1903.10247">arXiv:1903.10247</a>)</p> </li> </ul> <div class="footnotes"><hr /><ol><li id="fn:1"> <p>Here <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math> denotes the <a class="existingWikiWord" href="/nlab/show/exponent">exponent</a> with which the brane’s <a class="existingWikiWord" href="/nlab/show/tension">tension</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>T</mi></mrow><annotation encoding="application/x-tex">T</annotation></semantics></math> scales with the <a class="existingWikiWord" href="/nlab/show/string+coupling+constant">string coupling constant</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>g</mi> <mi>s</mi></msub></mrow><annotation encoding="application/x-tex">g_s</annotation></semantics></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>T</mi><mo>∝</mo><mo stretchy="false">(</mo><msub><mi>g</mi> <mi>s</mi></msub><msup><mo stretchy="false">)</mo> <mi>α</mi></msup></mrow><annotation encoding="application/x-tex">T \propto (g_s)^\alpha</annotation></semantics></math>, according to <a href="#BMO19">BMO 2019</a>, <a href="https://arxiv.org/pdf/1903.10247.pdf#page=2">p. 2</a>. <a href="#fnref:1" rev="footnote">↩</a></p> </li></ol></div></body></html> </div> <div class="revisedby"> <p> Last revised on July 2, 2023 at 14:20:17. See the <a href="/nlab/history/exotic+brane" style="color: #005c19">history</a> of this page for a list of all contributions to it. </p> </div> <div class="navigation navfoot"> <a href="/nlab/edit/exotic+brane" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussion/11256/#Item_9">Discuss</a><span class="backintime"><a href="/nlab/revision/exotic+brane/9" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/exotic+brane" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/exotic+brane" accesskey="S" class="navlink" id="history" rel="nofollow">History (9 revisions)</a> <a href="/nlab/show/exotic+brane/cite" style="color: black">Cite</a> <a href="/nlab/print/exotic+brane" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/exotic+brane" id="view_source" rel="nofollow">Source</a> </div> </div> <!-- Content --> </div> <!-- Container --> </body> </html>