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black brane in nLab
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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/3218/#Item_4" 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="gravity">Gravity</h4> <div class="hide"><div> <p><strong><a class="existingWikiWord" href="/nlab/show/gravity">gravity</a>, <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></strong></p> <p><strong>Formalism</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Poincar%C3%A9+Lie+algebra">Poincaré Lie algebra</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/super+Poincar%C3%A9+Lie+algebra">super Poincaré Lie algebra</a>, <a class="existingWikiWord" href="/nlab/show/supergravity+Lie+3-algebra">supergravity Lie 3-algebra</a>, <a class="existingWikiWord" href="/nlab/show/supergravity+Lie+6-algebra">supergravity Lie 6-algebra</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/differential+geometry">differential geometry</a></p> </li> <li> <p>(<a class="existingWikiWord" href="/nlab/show/super-Cartan+geometry">super</a>-)<a class="existingWikiWord" href="/nlab/show/Cartan+geometry">Cartan geometry</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/pseudo-Riemannian+manifold">pseudo</a>-<a class="existingWikiWord" href="/nlab/show/Riemannian+manifold">Riemannian manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> </li> </ul> </li> </ul> <p><strong>Definition</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Einstein-Hilbert+action">Einstein-Hilbert action</a>, <a class="existingWikiWord" href="/nlab/show/Einstein%27s+equations">Einstein's equations</a>, <a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a>, <a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a>, <a class="existingWikiWord" href="/nlab/show/Plebanski+formulation+of+gravity">Plebanski formulation of gravity</a>, <a class="existingWikiWord" href="/nlab/show/teleparallel+gravity">teleparallel gravity</a></p> </li> </ul> </li> </ul> <p><strong>Spacetime configurations</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Minkowski+spacetime">Minkowski spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+hole+spacetime">black hole spacetime</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Schwarzschild+spacetime">Schwarzschild spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kerr+spacetime">Kerr spacetime</a></p> </li> </ul> </li> </ul> <p><strong>Properties</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bekenstein-Hawking+entropy">Bekenstein-Hawking entropy</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/generalized+second+law+of+thermodynamics">generalized second law of thermodynamics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/cosmic+censorship+hypothesis">cosmic censorship hypothesis</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/weak+gravity+conjecture">weak gravity conjecture</a></p> </li> </ul> <p><strong>Spacetimes</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/standard+model+of+cosmology">standard model of cosmology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Minkowski+spacetime">Minkowski spacetime</a></p> </li> </ul> <div> <table><thead><tr><th><strong><a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a> <a class="existingWikiWord" href="/nlab/show/spacetimes">spacetimes</a></strong></th><th>vanishing <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a></th><th><a class="existingWikiWord" href="/nlab/show/positive+number">positive</a> <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a></th></tr></thead><tbody><tr><td style="text-align: left;"><strong>vanishing <a class="existingWikiWord" href="/nlab/show/charge">charge</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Schwarzschild+spacetime">Schwarzschild spacetime</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Kerr+spacetime">Kerr spacetime</a></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/positive+number">positive</a> <a class="existingWikiWord" href="/nlab/show/charge">charge</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Reissner-Nordstrom+spacetime">Reissner-Nordstrom spacetime</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/Kerr-Newman+spacetime">Kerr-Newman spacetime</a></td></tr> </tbody></table> </div> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/asymptotically+flat+spacetime">asymptotically flat spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravitational+wave">gravitational wave</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/anti+de+Sitter+spacetime">anti de Sitter spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/FRW+spacetime">FRW spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Taub-NUT+spacetime">Taub-NUT spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Einstein+manifold">Einstein manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/pp-wave+spacetime">pp-wave spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/KK-monopole">KK-monopole</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Malament%E2%80%93Hogarth+spacetime">Malament–Hogarth spacetime</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/super+spacetime">super spacetime</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/super+Minkowski+spacetime">super Minkowski spacetime</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+brane">black brane</a></p> </li> </ul> <p><strong>Quantum theory</strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+gravity">quantum gravity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/graviton">graviton</a>, <a class="existingWikiWord" href="/nlab/show/gravitino">gravitino</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a></p> </li> </ul> </li> </ul> </div></div> <h4 id="physics">Physics</h4> <div class="hide"><div> <p><strong><a class="existingWikiWord" href="/nlab/show/physics">physics</a></strong>, <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>, <a class="existingWikiWord" href="/nlab/show/philosophy+of+physics">philosophy of physics</a></p> <h2 id="surveys_textbooks_and_lecture_notes">Surveys, textbooks and lecture notes</h2> <ul> <li> <p><em><a class="existingWikiWord" href="/nlab/show/higher+category+theory+and+physics">(higher) category theory and physics</a></em></p> </li> <li> <p><em><a class="existingWikiWord" href="/nlab/show/geometry+of+physics">geometry of physics</a></em></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/books+and+reviews+in+mathematical+physics">books and reviews</a>, <a class="existingWikiWord" href="/nlab/show/physics+resources">physics resources</a></p> </li> </ul> <hr /> <p><a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory (physics)</a>, <a class="existingWikiWord" href="/nlab/show/model+%28physics%29">model (physics)</a></p> <p><a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>, <a class="existingWikiWord" href="/nlab/show/measurement">measurement</a>, <a class="existingWikiWord" href="/nlab/show/computable+physics">computable physics</a></p> <ul> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/mechanics">mechanics</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/mass">mass</a>, <a class="existingWikiWord" href="/nlab/show/charge">charge</a>, <a class="existingWikiWord" href="/nlab/show/momentum">momentum</a>, <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a>, <a class="existingWikiWord" href="/nlab/show/moment+of+inertia">moment of inertia</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/dynamics+on+Lie+groups">dynamics on Lie groups</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/rigid+body+dynamics">rigid body dynamics</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/field+%28physics%29">field (physics)</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Lagrangian+mechanics">Lagrangian mechanics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/configuration+space">configuration space</a>, <a class="existingWikiWord" href="/nlab/show/state">state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/action+functional">action functional</a>, <a class="existingWikiWord" href="/nlab/show/Lagrangian">Lagrangian</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/covariant+phase+space">covariant phase space</a>, <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+equations">Euler-Lagrange equations</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Hamiltonian+mechanics">Hamiltonian mechanics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/phase+space">phase space</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+geometry">symplectic geometry</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Poisson+manifold">Poisson manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+manifold">symplectic manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+groupoid">symplectic groupoid</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/multisymplectic+geometry">multisymplectic geometry</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/n-symplectic+manifold">n-symplectic manifold</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/smooth+Lorentzian+manifold">smooth Lorentzian manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/special+relativity">special relativity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity">gravity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, <a class="existingWikiWord" href="/nlab/show/dilaton+gravity">dilaton gravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a></p> </li> </ul> </li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/classical+field+theory">Classical field theory</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/classical+physics">classical physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/classical+mechanics">classical mechanics</a></li> <li><a class="existingWikiWord" href="/nlab/show/waves">waves</a> and <a class="existingWikiWord" href="/nlab/show/optics">optics</a></li> <li><a class="existingWikiWord" href="/nlab/show/thermodynamics">thermodynamics</a></li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+mechanics">Quantum Mechanics</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+mechanics+in+terms+of+dagger-compact+categories">in terms of ∞-compact categories</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+information">quantum information</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Hamiltonian+operator">Hamiltonian operator</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a></p> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantization">Quantization</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/geometric+quantization">geometric quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/deformation+quantization">deformation quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/path+integral">path integral quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/semiclassical+approximation">semiclassical approximation</a></p> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+field+theory">Quantum Field Theory</a></strong></p> <ul> <li> <p>Axiomatizations</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/AQFT">algebraic QFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Wightman+axioms">Wightman axioms</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Haag-Kastler+axioms">Haag-Kastler axioms</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/operator+algebra">operator algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/local+net">local net</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/conformal+net">conformal net</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Reeh-Schlieder+theorem">Reeh-Schlieder theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Osterwalder-Schrader+theorem">Osterwalder-Schrader theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/PCT+theorem">PCT theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bisognano-Wichmann+theorem">Bisognano-Wichmann theorem</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/modular+theory">modular theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spin-statistics+theorem">spin-statistics theorem</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/boson">boson</a>, <a class="existingWikiWord" href="/nlab/show/fermion">fermion</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/FQFT">functorial QFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/cobordism">cobordism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2Cn%29-category+of+cobordisms">(∞,n)-category of cobordisms</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/cobordism+hypothesis">cobordism hypothesis</a>-theorem</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/extended+topological+quantum+field+theory">extended topological quantum field theory</a></p> </li> </ul> </li> </ul> </li> <li> <p>Tools</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a>, <a class="existingWikiWord" href="/nlab/show/vacuum">vacuum</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/effective+quantum+field+theory">effective quantum field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/renormalization">renormalization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/BV-BRST+formalism">BV-BRST formalism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/geometric+%E2%88%9E-function+theory">geometric ∞-function theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/model+%28in+particle+phyiscs%29">models</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/fields+and+quanta+-+table">fields and quanta</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/GUT">Grand Unified Theories</a>, <a class="existingWikiWord" href="/nlab/show/MSSM">MSSM</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/on-shell+recursion">on-shell recursion</a>, <a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></li> </ul> </li> </ul> </li> <li> <p>Structural phenomena</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/universality+class">universality class</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+anomaly">quantum anomaly</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Green-Schwarz+mechanism">Green-Schwarz mechanism</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/instanton">instanton</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spontaneously+broken+symmetry">spontaneously broken symmetry</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/integrable+systems">integrable systems</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/holonomic+quantum+fields">holonomic quantum fields</a></p> </li> </ul> </li> <li> <p>Types of quantum field thories</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/TQFT">TQFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/2d+TQFT">2d TQFT</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Dijkgraaf-Witten+theory">Dijkgraaf-Witten theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Chern-Simons+theory">Chern-Simons theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/TCFT">TCFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/A-model">A-model</a>, <a class="existingWikiWord" href="/nlab/show/B-model">B-model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/homological+mirror+symmetry">homological mirror symmetry</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/QFT+with+defects">QFT with defects</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/conformal+field+theory">conformal field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%281%2C1%29-dimensional+Euclidean+field+theories+and+K-theory">(1,1)-dimensional Euclidean field theories and K-theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%282%2C1%29-dimensional+Euclidean+field+theory">(2,1)-dimensional Euclidean field theory and elliptic cohomology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/CFT">CFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/WZW+model">WZW model</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> <li> <p><a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/field+strength">field strength</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gauge+group">gauge group</a>, <a class="existingWikiWord" href="/nlab/show/gauge+transformation">gauge transformation</a>, <a class="existingWikiWord" href="/nlab/show/gauge+fixing">gauge fixing</a></p> </li> <li> <p>examples</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/electromagnetic+field">electromagnetic field</a>, <a class="existingWikiWord" href="/nlab/show/QED">QED</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/electric+charge">electric charge</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/magnetic+charge">magnetic charge</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yang-Mills+field">Yang-Mills field</a>, <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spinors+in+Yang-Mills+theory">spinors in Yang-Mills theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+Yang-Mills+theory">topological Yang-Mills theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Kalb-Ramond+field">Kalb-Ramond field</a></li> <li><a class="existingWikiWord" href="/nlab/show/supergravity+C-field">supergravity C-field</a></li> <li><a class="existingWikiWord" href="/nlab/show/RR+field">RR field</a></li> <li><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/general+covariance">general covariance</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/particle">particle</a>, <a class="existingWikiWord" href="/nlab/show/relativistic+particle">relativistic particle</a>, <a class="existingWikiWord" href="/nlab/show/fundamental+particle">fundamental particle</a>, <a class="existingWikiWord" href="/nlab/show/spinning+particle">spinning particle</a>, <a class="existingWikiWord" href="/nlab/show/superparticle">superparticle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string">string</a>, <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/membrane">membrane</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/AKSZ+theory">AKSZ theory</a></p> </li> </ul> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+theory">String Theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/string+theory+results+applied+elsewhere">string theory results applied elsewhere</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/number+theory+and+physics">number theory and physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Riemann+hypothesis+and+physics">Riemann hypothesis and physics</a></li> </ul> </li> </ul> <div> <p> <a href="/nlab/edit/physicscontents">Edit this sidebar</a> </p> </div></div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#properties'>Properties</a></li> <ul> <li><a href='#weak_coupling_correspondence'>Weak coupling correspondence</a></li> </ul> <li><a href='#examples'>Examples</a></li> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#References'>References</a></li> <ul> <li><a href='#ReferencesMatchingKNBlackHolesToElementaryParticles'>Matching KN black holes to elementary particles</a></li> <li><a href='#ReferencesGeneral'>Black branes in supergravity</a></li> <li><a href='#blackfold_approach'>Blackfold approach</a></li> <li><a href='#ReferencesMicroscopicAdSCFTViapBraneSigmaModesl'>Microscopic AdS/CFT via <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>-brane sigma-models</a></li> </ul> </ul> </div> <h2 id="idea">Idea</h2> <p>The theory of <a class="existingWikiWord" href="/nlab/show/gravity">gravity</a> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">3+1</annotation></semantics></math> dimensions famously has <a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a> solutions, being the limiting configuration of a <em>point</em> mass gravitational source. In higher dimensional gravity, and in particular in higher dimensional <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, there are analogous solutions, which however are limiting configurations of a gravitational source that is supported on a line, or a surface, or a higher dimensional space. For a surface one might speak of <em>black <a class="existingWikiWord" href="/nlab/show/membrane">membrane</a></em> solutions hence generally of <em>black brane</em> solutions.</p> <p>Particularly the <a class="existingWikiWord" href="/nlab/show/BPS+states">BPS states</a> among the black branes in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, i.e. those solutions that carry <a class="existingWikiWord" href="/nlab/show/Killing+spinors">Killing spinors</a>, include configurations that look like the strong-coupling version of the <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+super+p-branes">Green-Schwarz super p-branes</a>.</p> <div> <p><strong>1/2 <a class="existingWikiWord" href="/nlab/show/BPS+state">BPS</a> <a class="existingWikiWord" href="/nlab/show/black+branes">black branes</a> in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></strong>: <a class="existingWikiWord" href="/nlab/show/D-branes">D-branes</a>, <a class="existingWikiWord" href="/nlab/show/F1-brane">F1-brane</a>, <a class="existingWikiWord" href="/nlab/show/NS5-brane">NS5-brane</a>, <a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a>, <a class="existingWikiWord" href="/nlab/show/M5-brane">M5-brane</a></p> <p><img width="600" src="http://ncatlab.org/nlab/files/BraneSolutionsInSupergravity.jpg" /></p> <blockquote> <p>(table from <a href="black+brane#BlumenhagenLustTheisen13">Blumenhagen, Lüst & Theisen 2013, Chapter 18.5</a>)</p> </blockquote> </div> <p>The <a class="existingWikiWord" href="/nlab/show/near-horizon+geometry">near-horizon geometry</a> of these black branes is generically that of <a class="existingWikiWord" href="/nlab/show/anti+de+Sitter+spacetime">anti de Sitter spacetime</a> times a <a class="existingWikiWord" href="/nlab/show/sphere">sphere</a>. To the extent that the <a class="existingWikiWord" href="/nlab/show/worldvolume">worldvolume</a> theory of the branes is a <a class="existingWikiWord" href="/nlab/show/superconformal+QFT">superconformal QFT</a>, this is the origin of the <a class="existingWikiWord" href="/nlab/show/AdS-CFT+correspondence">AdS-CFT correspondence</a>.</p> <h2 id="properties">Properties</h2> <h3 id="weak_coupling_correspondence">Weak coupling correspondence</h3> <p>The types of black branes that can occur in theories of <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> that are obtained from the maximal <a class="existingWikiWord" href="/nlab/show/11-dimensional+supergravity">11-dimensional supergravity</a> match precisely the types of <a class="existingWikiWord" href="/nlab/show/D-brane">D-brane</a>s and <a class="existingWikiWord" href="/nlab/show/NS-brane">NS-brane</a>s that appear in the corresponding perturbative <a class="existingWikiWord" href="/nlab/show/superstring+theories">superstring theories</a>.</p> <p>The idea is that both these brane-phenomena are aspects of one single entity:</p> <ul> <li> <p>At low <a class="existingWikiWord" href="/nlab/show/string+coupling">string coupling</a> the <a class="existingWikiWord" href="/nlab/show/D-brane">D-brane</a>/<a class="existingWikiWord" href="/nlab/show/NS-brane">NS-brane</a> description is accurate. Low <a class="existingWikiWord" href="/nlab/show/string+coupling">string coupling</a> implies that the coupling of <a class="existingWikiWord" href="/nlab/show/gravity">gravity</a> is weak, hence that the back-reaction of the branes on the background geometry is negligible.</p> </li> <li> <p>At large <a class="existingWikiWord" href="/nlab/show/string+coupling">string coupling</a> but low <a class="existingWikiWord" href="/nlab/show/energy">energy</a>, the <a class="existingWikiWord" href="/nlab/show/effective+field+theory">effective</a> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> description becomes accurate. Here the branes do back-react on the gravitational background and hence create the <em>black brane</em> spacetime geometry.</p> </li> </ul> <p>This duality of the brane picture is at the heart of the <a class="existingWikiWord" href="/nlab/show/AdS%2FCFT+correspondence">AdS/CFT correspondence</a>. See there for more details.</p> <h2 id="examples">Examples</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a>, <a class="existingWikiWord" href="/nlab/show/black+hole+in+string+theory">black hole in string theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+string">black string</a></p> </li> <li> <p><span class="newWikiWord">black membrane<a href="/nlab/new/black+membrane">?</a></span></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+fivebrane">black fivebrane</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+triple+junction">string triple junction</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/membrane+triple+junction">membrane triple junction</a></p> </li> </ul> <h2 id="related_concepts">Related concepts</h2> <div> <p><strong>Table of <a class="existingWikiWord" href="/nlab/show/brane">branes</a> appearing in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>/<a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a></strong> (for classification see at <em><a class="existingWikiWord" href="/nlab/show/brane+scan">brane scan</a></em>).</p> <table><thead><tr><th><a class="existingWikiWord" href="/nlab/show/brane">brane</a></th><th>in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></th><th><a class="existingWikiWord" href="/nlab/show/charge">charge</a>d under <a class="existingWikiWord" href="/nlab/show/gauge+field">gauge field</a></th><th>has <a class="existingWikiWord" href="/nlab/show/worldvolume">worldvolume</a> theory</th></tr></thead><tbody><tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/black+brane">black brane</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/higher+gauge+field">higher gauge field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/SCFT">SCFT</a></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/D-brane">D-brane</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/type+II+supergravity">type II</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/RR-field">RR-field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/super+Yang-Mills+theory">super Yang-Mills theory</a></td></tr> <tr><td style="text-align: left;"><strong><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mi>D</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(D = 2n)</annotation></semantics></math></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/type+IIA+supergravity">type IIA</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D%28-2%29-brane">D(-2)-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D0-brane">D0-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/BFSS+matrix+model">BFSS matrix model</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D2-brane">D2-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D4-brane">D4-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D%3D5+super+Yang-Mills+theory">D=5 super Yang-Mills theory</a> with <a class="existingWikiWord" href="/nlab/show/Khovanov+homology">Khovanov homology</a> <a class="existingWikiWord" href="/nlab/show/observables">observables</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D6-brane">D6-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D%3D7+super+Yang-Mills+theory">D=7 super Yang-Mills theory</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D8-brane">D8-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><strong><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mi>D</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(D = 2n+1)</annotation></semantics></math></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/type+IIB+supergravity">type IIB</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D%28-1%29-brane">D(-1)-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D1-brane">D1-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;">2d <a class="existingWikiWord" href="/nlab/show/CFT">CFT</a> with <a class="existingWikiWord" href="/nlab/show/BH+entropy">BH entropy</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D3-brane">D3-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/N%3D4+D%3D4+super+Yang-Mills+theory">N=4 D=4 super Yang-Mills theory</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D5-brane">D5-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D7-brane">D7-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D9-brane">D9-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/%28p%2Cq%29-string">(p,q)-string</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;">(<a class="existingWikiWord" href="/nlab/show/D25-brane">D25-brane</a>)</td><td style="text-align: left;">(<a class="existingWikiWord" href="/nlab/show/bosonic+string+theory">bosonic string theory</a>)</td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/NS-brane">NS-brane</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/supergravity">type I, II, heterotic</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/circle+n-bundle+with+connection">circle n-connection</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/string">string</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/B2-field">B2-field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/2d+SCFT">2d SCFT</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/NS5-brane">NS5-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/B6-field">B6-field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/little+string+theory">little string theory</a></td></tr> <tr><td style="text-align: left;"><strong>D-brane for <a class="existingWikiWord" href="/nlab/show/topological+string">topological string</a></strong></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/A-brane">A-brane</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/B-brane">B-brane</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/M-brane">M-brane</a></strong></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/11-dimensional+supergravity">11D SuGra</a>/<a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/circle+n-bundle+with+connection">circle n-connection</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/C3-field">C3-field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/ABJM+theory">ABJM theory</a>, <a class="existingWikiWord" href="/nlab/show/BLG+model">BLG model</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/M5-brane">M5-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/C6-field">C6-field</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-superconformal+QFT">6d (2,0)-superconformal QFT</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/M9-brane">M9-brane</a>/<a class="existingWikiWord" href="/nlab/show/O-plane">O9-plane</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/heterotic+string+theory">heterotic string theory</a></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/M-wave">M-wave</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/topological+M2-brane">topological M2-brane</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/topological+M-theory">topological M-theory</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/C3-field">C3-field</a> on <a class="existingWikiWord" href="/nlab/show/G%E2%82%82-manifold">G₂-manifold</a></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/topological+M5-brane">topological M5-brane</a></td><td style="text-align: left;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/C6-field">C6-field</a> on <a class="existingWikiWord" href="/nlab/show/G%E2%82%82-manifold">G₂-manifold</a></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/S-brane">S-brane</a></strong></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/SM2-brane">SM2-brane</a>,<br /><a class="existingWikiWord" href="/nlab/show/membrane+instanton">membrane instanton</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/M5-brane+instanton">M5-brane instanton</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/D3-brane+instanton">D3-brane instanton</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><strong><a class="existingWikiWord" href="/nlab/show/solitons">solitons</a></strong> on <a class="existingWikiWord" href="/nlab/show/M5-brane">M5-brane</a></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-superconformal+QFT">6d (2,0)-superconformal QFT</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/self-dual+string">self-dual string</a></td><td style="text-align: left;"></td><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/self-dual+higher+gauge+field">self-dual</a> <a class="existingWikiWord" href="/nlab/show/B-field">B-field</a></td><td style="text-align: left;"></td></tr> <tr><td style="text-align: left;"><a class="existingWikiWord" href="/nlab/show/3-brane+in+6d">3-brane in 6d</a></td><td style="text-align: left;"></td><td style="text-align: left;"></td><td style="text-align: left;"></td></tr> </tbody></table> </div> <h2 id="References">References</h2> <p>By “black branes” one mostly refers to – generally higher-dimensional – singular solutions of theories of <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, referenced below at</p> <ul> <li><em><a href="#ReferencesGeneral">Black branes in supergravity</a></em></li> </ul> <p>But closely related discussion has historically been had on the possibility of identifying <a class="existingWikiWord" href="/nlab/show/electrons">electrons</a> and other <a class="existingWikiWord" href="/nlab/show/fundamental+particles">fundamental particles</a> with <a class="existingWikiWord" href="/nlab/show/Kerr-Newman+black+hole">Kerr-Newman</a> <a class="existingWikiWord" href="/nlab/show/black+holes">black holes</a> (“black 0-branes”):</p> <div> <h3 id="ReferencesMatchingKNBlackHolesToElementaryParticles">Matching KN black holes to elementary particles</h3> <p>On the similarity between <a class="existingWikiWord" href="/nlab/show/Kerr-Newman+black+holes">Kerr-Newman black holes</a> (charged and spinning “<a class="existingWikiWord" href="/nlab/show/black+brane">black 0-branes</a>”) and <a class="existingWikiWord" href="/nlab/show/elementary+particles">elementary particles</a> (<a class="existingWikiWord" href="/nlab/show/super+p-brane">sigma-model 0-branes</a>) like <a class="existingWikiWord" href="/nlab/show/electrons">electrons</a>.</p> <p>Historical precursor discussion on the possibility of <em><a class="existingWikiWord" href="/nlab/show/geometrodynamics">geometrodynamics</a></em> for <a class="existingWikiWord" href="/nlab/show/fundamental+particles">fundamental particles</a>:</p> <ul> <li id="EinsteinInfeldHoffmann39"><a class="existingWikiWord" href="/nlab/show/Albert+Einstein">Albert Einstein</a>, <a class="existingWikiWord" href="/nlab/show/Leopold+Infeld">Leopold Infeld</a>, B. Hoffmann, <em>The gravitational equations and the problem of motion</em>, Annals of Mathematics <strong>39</strong> 1 (1938) [<a href="https://doi.org/10.2307/1968714">doi:10.2307/1968714</a>, <a href="https://www.jstor.org/stable/1968714">jstor:1968714</a>]</li> </ul> <p>Seminal observation that the gyromagnetic ratio of the <a class="existingWikiWord" href="/nlab/show/Kerr-Newman+black+hole">Kerr-Newman black hole</a> is 2, just as the for <a class="existingWikiWord" href="/nlab/show/electron">electron</a> (cf. at <em><a class="existingWikiWord" href="/nlab/show/anomalous+magnetic+moment">anomalous magnetic moment</a></em>):</p> <ul> <li> <p>Brandon Carter, p. 1562 of: <em>Global Structure of the Kerr Family of Gravitational Fields</em>, Phys. Rev. <strong>174</strong> (1968) 1559 [<a href="https://doi.org/10.1103/PhysRev.174.1559">doi:10.1103/PhysRev.174.1559</a>]</p> </li> <li> <p>Werner Israel, <em>Source of the Kerr Metric</em>, Phys. Rev. D <strong>2</strong> 641 (1970) [<a href="https://doi.org/10.1103/PhysRevD.2.641">doi:10.1103/PhysRevD.2.641</a>]</p> </li> </ul> <p>Further discussion:</p> <ul> <li> <p>Carlos A. López, <em>Extended model of the electron in general relativity</em>, Phys. Rev. D <strong>30</strong> 313 (1984) [<a href="https://doi.org/10.1103/PhysRevD.30.313">doi:10.1103/PhysRevD.30.313<a>]</a></a></p> </li> <li> <p>H. I. Arcos, J. G. Pereira: <em>Kerr–Newman Solution as a Dirac Particle</em>, General Relativity and Gravitation <strong>36</strong> (2004) 2441–2464 [<a href="https://doi.org/10.1023/B:GERG.0000046832.71368.a5">doi:10.1023/B:GERG.0000046832.71368.a5</a>, <a href="https://arxiv.org/abs/hep-th/0210103">arXiv:hep-th/0210103</a>]</p> </li> <li> <p>Alexander Burinskii, <em>The Dirac-Kerr-Newman electron</em>, Gravit. Cosmol. <strong>14</strong> (2008) 109–122 [<a href="https://doi.org/10.1134/S0202289308020011">doi:10.1134/S0202289308020011</a>, <a href="https://arxiv.org/abs/hep-th/0507109">arXiv:hep-th/0507109</a>]</p> </li> <li> <p>Alexander Burinskii, <em>Kerr–Newman electron as spinning soliton</em>, International Journal of Modern Physics A <strong>29</strong> 26, 1450133 (2014) [<a href="https://doi.org/10.1142/S0217751X14501334">doi:10.1142/S0217751X14501334</a>, <a href="https://arxiv.org/abs/1410.2888">arXiv:1410.2888</a>]</p> </li> </ul> <p>See also:</p> <ul> <li>Wikipedia, <em><a href="https://en.wikipedia.org/wiki/Black_hole_electron">Black hole electron</a></em></li> </ul> </div> <h3 id="ReferencesGeneral">Black branes in supergravity</h3> <p>Original articles on black branes in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> (and thereby in <a class="existingWikiWord" href="/nlab/show/string+theory">string</a>/<a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a>):</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Ramzi+R.+Khuri">Ramzi R. Khuri</a>, <a class="existingWikiWord" href="/nlab/show/Jian+Xin+Lu">Jian Xin Lu</a>, <em>String and Fivebrane Solitons: Singular or Non-singular?</em>, Nucl.Phys. B <strong>377</strong> (1992) 281-294 [<a href="https://arxiv.org/abs/hep-th/9112023">arXiv:hep-th/9112023</a>, <a href="https://doi.org/10.1016/0550-3213(92)90025-7">doi:10.1016/0550-3213(92)90025-7</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Jian+Xin+Lu">Jian Xin Lu</a>, <em>Black and super <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>-branes in diverse dimensions</em>, Nucl. Phys. B <strong>416</strong> (1994) 301-334 [<a href="http://arxiv.org/abs/hep-th/9306052">arXiv:hep-th/9306052</a>, <a href="https://doi.org/10.1016/0550-3213(94)90586-X">doi:10.1016/0550-3213(94)90586-X</a>]</p> </li> <li id="DuffKhuriLu94"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <a class="existingWikiWord" href="/nlab/show/Ramzi+R.+Khuri">Ramzi R. Khuri</a>, <a class="existingWikiWord" href="/nlab/show/Jian+Xin+Lu">Jian Xin Lu</a>, <em>String Solitons</em>, Phys. Rept. <strong>259</strong> (1995) 213-326 [<a href="https://arxiv.org/abs/hep-th/9412184">arXiv:hep-th/9412184</a>, <a href="https://doi.org/10.1016/0370-1573(95)00002-X">doi:10.1016/0370-1573(95)00002-X</a>]</p> <blockquote> <p>(<a class="existingWikiWord" href="/nlab/show/solitonic+branes">solitonic branes</a>)</p> </blockquote> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, H. Lu, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <em>The Black Branes of M-theory</em>, Phys. Lett. B <strong>382</strong> (1996) [<a href="http://arxiv.org/abs/hep-th/9604052">arXiv:hep-th/9604052</a>]</p> </li> </ul> <p>The <a class="existingWikiWord" href="/nlab/show/M5-brane">M5-brane</a> was maybe first found as a black brane of <a class="existingWikiWord" href="/nlab/show/11-dimensional+supergravity">11-dimensional supergravity</a> (the <a class="existingWikiWord" href="/nlab/show/black+fivebrane">black fivebrane</a>) in</p> <ul> <li id="Gueven92"><a class="existingWikiWord" href="/nlab/show/Rahmi+Gueven">Rahmi Gueven</a>, <em>Black <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>-brane solutions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>D</mi><mo>=</mo><mn>11</mn></mrow><annotation encoding="application/x-tex">D = 11</annotation></semantics></math> supergravity theory, Phys. Lett. B276 (1992) 49 and in <a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a> (ed.)</em><a class="existingWikiWord" href="/nlab/show/The+World+in+Eleven+Dimensions">The World in Eleven Dimensions</a>_ 135-141 (<a href="http://inspirehep.net/record/338203">spire:338203</a>)</li> </ul> <p>The observation that black <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>-branes metric for <em>odd</em> <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> are completely non-singular is due to</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Gary+Gibbons">Gary Gibbons</a>, <a class="existingWikiWord" href="/nlab/show/Gary+Horowitz">Gary Horowitz</a>, <a class="existingWikiWord" href="/nlab/show/Paul+Townsend">Paul Townsend</a>, p. 15 of <em>Higher-dimensional resolution of dilatonic black hole singularities</em>, Class. Quant. Grav.12:297-318,1995 (<a href="https://arxiv.org/abs/hep-th/9410073">arXiv:hep-th/9410073</a>)</li> </ul> <p>The suggestion that extremal/<a class="existingWikiWord" href="/nlab/show/BPS+state">BPS state</a> black branes are the strong coupling incarnation of fundamental branes originates in</p> <ul> <li id="HullTownsend94"> <p><a class="existingWikiWord" href="/nlab/show/Chris+Hull">Chris Hull</a>, <a class="existingWikiWord" href="/nlab/show/Paul+Townsend">Paul Townsend</a>, <em>Unity of Superstring Dualities</em>, Nucl. Phys. B <strong>438</strong> (1995) 109-137 [<a href="http://arxiv.org/abs/hep-th/9410167">arXiv:hep-th/9410167</a>]</p> </li> <li id="Witten95"> <p><a class="existingWikiWord" href="/nlab/show/Edward+Witten">Edward Witten</a>, p. 6 (bottom) of: <em>String Theory Dynamics In Various Dimensions</em>, Nucl. Phys. B <strong>443</strong> (1995) 85-126 [<a href="http://arxiv.org/abs/hep-th/9503124">arXiv:hep-th/9503124</a>]</p> </li> </ul> <p>Review:</p> <ul> <li id="Duff99"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, chapter 5 of: <em><a class="existingWikiWord" href="/nlab/show/The+World+in+Eleven+Dimensions">The World in Eleven Dimensions</a>: Supergravity, Supermembranes and M-theory</em>, IoP (1999) [<a href="https://www.crcpress.com/The-World-in-Eleven-Dimensions-Supergravity-supermembranes-and-M-theory/Duff/9780750306720">ISBN:9780750306720</a>]</p> </li> <li id="Stelle98"> <p><a class="existingWikiWord" href="/nlab/show/Kellogg+Stelle">Kellogg Stelle</a>, around section 3.3 of: <em>BPS Branes in Supergravity</em>, in: <em>Quantum Field Theory: Perspective and Prospective</em>, NATO Science Series <strong>530</strong> (1999) 257-351 [<a href="http://arxiv.org/abs/hep-th/9803116">arXiv:hep-th/9803116</a>, <a href="https://doi.org/10.1007/978-94-011-4542-8_12">doi:10.1007/978-94-011-4542-8_12</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Ofer+Aharony">Ofer Aharony</a>, S. S. Gubser, <a class="existingWikiWord" href="/nlab/show/Juan+Maldacena">Juan Maldacena</a>, H. Ooguri, Y. Oz, section 1.3 of <em>Large N Field Theories, String Theory and Gravity</em> [<a href="http://arxiv.org/abs/hep-th/9905111">arXiv:hep-th/9905111</a>]</p> </li> <li id="Mohaupt00"> <p><a class="existingWikiWord" href="/nlab/show/Thomas+Mohaupt">Thomas Mohaupt</a>, <em>Black holes in supergravity and string theory</em>, Class. Quantum Grav. 17 (2000) 3429–3482 (<a href="http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Mohaupt_CQG_2000.pdf">pdf</a>)</p> </li> <li id="BlumenhagenLustTheisen13"> <p><a class="existingWikiWord" href="/nlab/show/Ralph+Blumenhagen">Ralph Blumenhagen</a>, <a class="existingWikiWord" href="/nlab/show/Dieter+L%C3%BCst">Dieter Lüst</a>, <a class="existingWikiWord" href="/nlab/show/Stefan+Theisen">Stefan Theisen</a>, <em>Brane solutions in supergravity</em>, chapter 18.5 in: <em>Basic Concepts of String Theory</em>, Springer (2013) [<a href="https://doi.org/10.1007/978-3-642-29497-6">doi:10.1007/978-3-642-29497-6</a>]</p> </li> </ul> <p>and in the context of multiple <a class="existingWikiWord" href="/nlab/show/M2-branes">M2-branes</a> in the <a class="existingWikiWord" href="/nlab/show/BLG+model">BLG model</a>:</p> <ul> <li id="BaggerLambert12"><a class="existingWikiWord" href="/nlab/show/Jonathan+Bagger">Jonathan Bagger</a>, <a class="existingWikiWord" href="/nlab/show/Neil+Lambert">Neil Lambert</a>, <a class="existingWikiWord" href="/nlab/show/Sunil+Mukhi">Sunil Mukhi</a>, Constantinos Papageorgakis, section 1.6 of <em>Multiple Membranes in M-theory</em> (<a href="http://arxiv.org/abs/1203.3546">arXiv:1203.3546</a>)</li> </ul> <p>Further developments include</p> <ul> <li> <p>Gerard Clement, Dmitri Gal’tsov, Cedric Leygnac, <em>Black branes on the linear dilaton background</em>, Phys. Rev. D71 (2005) 084014 (<a href="http://arxiv.org/abs/hep-th/0412321">arXiv:hep-th/0412321</a>)</p> </li> <li> <p>D. Gal’tsov, S. Klevtsov, D. Orlov, G. Clement, <em>More on general <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>-brane solutions</em>, Int.J.Mod.Phys.A21:3575-3604, 2006 (<a href="http://arxiv.org/abs/hep-th/0508070">arXiv:hep-th/0508070</a>)</p> </li> <li id="Duff08"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Near-horizon brane scan revived</em>, Nucl. Phys. B810:193-209, 2009 (<a href="http://arxiv.org/abs/0804.3675">arXiv:0804.3675</a>)</p> </li> <li> <p>Jay Armas, Joan Camps, Troels Harmark, Niels A. Obers, <em>The Young Modulus of Black Strings and the Fine Structure of Blackfolds</em> (<a href="http://arxiv.org/abs/1110.4835">arXiv:1110.4835</a>)</p> </li> </ul> <h3 id="blackfold_approach">Blackfold approach</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Roberto+Emparan">Roberto Emparan</a>, <a class="existingWikiWord" href="/nlab/show/Troels+Harmark">Troels Harmark</a>, <a class="existingWikiWord" href="/nlab/show/Vasilis+Niarchos">Vasilis Niarchos</a>, <a class="existingWikiWord" href="/nlab/show/Niels+A.+Obers">Niels A. Obers</a>, <em>Essentials of Blackfold Dynamics</em>, JHEP 1003 063 (2010) [<a href="https://arxiv.org/abs/0910.1601">arXiv:0910.1601</a>, <a href="https://doi.org/10.1007/JHEP03(2010)063">doi:10.1007/JHEP03(2010)063</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Roberto+Emparan">Roberto Emparan</a>, <a class="existingWikiWord" href="/nlab/show/Troels+Harmark">Troels Harmark</a>, <a class="existingWikiWord" href="/nlab/show/Vasilis+Niarchos">Vasilis Niarchos</a>, <a class="existingWikiWord" href="/nlab/show/Niels+A.+Obers">Niels A. Obers</a>, <em>Blackfolds in Supergravity and String Theory</em>, JHEP 1108 (2011) 154 [<a href="https://arxiv.org/abs/1106.4428">arXiv:1106.4428</a><a href="https://doi.org/10.1007/JHEP08(2011)154">doi:10.1007/JHEP08(2011)154</a>]</p> </li> </ul> <div> <h3 id="ReferencesMicroscopicAdSCFTViapBraneSigmaModesl">Microscopic AdS/CFT via <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>-brane sigma-models</h3> <p>Over a decade before the <a href="AdS-CFT+correspondence#ReferencesOriginModernAdSCFTDUality">modern formulation</a> of the <a class="existingWikiWord" href="/nlab/show/AdS-CFT+correspondence">AdS-CFT correspondence</a>, a candicate “microscopic” explanation was observed:</p> <div class="float_right_image" style="margin: -20px 0px 0px 15px"> <img src="/nlab/files/pBraneNearBlackBrane-240624.jpg" width="400px" /> </div> <p><a class="existingWikiWord" href="/nlab/show/immersion">Immersing</a> the <a class="existingWikiWord" href="/nlab/show/worldvolume">worldvolume</a> of a <a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a> <a class="existingWikiWord" href="/nlab/show/super+p-brane">super <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>-brane</a> (hence a “light” <a class="existingWikiWord" href="/nlab/show/brane">brane</a> without <a class="existingWikiWord" href="/nlab/show/backreaction">backreaction</a>) along the <a class="existingWikiWord" href="/nlab/show/near+horizon+geometry">near horizon geometry</a> (an <a class="existingWikiWord" href="/nlab/show/anti+de+Sitter+spacetime">AdS</a> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> solution) of its own <a class="existingWikiWord" href="/nlab/show/black+brane">black brane</a> incarnation (hence the “heavy” incarnation of the same brane, causing <a class="existingWikiWord" href="/nlab/show/backreaction">backreaction</a>), its <a class="existingWikiWord" href="/nlab/show/worldvolume">worldvolume</a> fluctuations (after <a class="existingWikiWord" href="/nlab/show/super-diffeomorphism">super-diffeomorphism</a> <a class="existingWikiWord" href="/nlab/show/gauge+fixing">gauge fixing</a>) are described by the corresponding <a class="existingWikiWord" href="/nlab/show/superconformal+field+theory">superconformal field theory</a> (exhibited by <a class="existingWikiWord" href="/nlab/show/superconformal+multiplets">superconformal multiplets</a> such as “<em><a class="existingWikiWord" href="/nlab/show/supersingletons">supersingletons</a></em>”) [graphics from <a class="existingWikiWord" href="/schreiber/show/Holographic+M-Brane+Super-Embeddings">GSS24</a>].</p> <p>The original observation for the <a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a>:</p> <ul> <li id="BDPS87"> <p><a class="existingWikiWord" href="/nlab/show/Eric+Bergshoeff">Eric Bergshoeff</a>, <a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <a class="existingWikiWord" href="/nlab/show/Ergin+Sezgin">Ergin Sezgin</a>: <em>Supersymmetric Supermembrane Vacua and Singletons</em>, Phys. Lett. B <strong>199</strong> (1987) 69-74 [<a href="https://doi.org/10.1016/0370-2693(87)91465-1">doi:10.1016/0370-2693(87)91465-1</a>, <a href="https://inspirehep.net/literature/250244">InSpire:250244</a>]</p> </li> <li id="BlencoweDuff88"> <p><a class="existingWikiWord" href="/nlab/show/Miles+P.+Blencowe">Miles P. Blencowe</a>, <a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <em>Supersingletons</em>, Physics letters B, <strong>203</strong> 3 (1988) 229-236 [<a href="http://dx.doi.org/10.1016/0370-2693(88)90544-8">doi:10.1016/0370-2693(88)90544-8</a>, <a href="http://cds.cern.ch/record/184143">cds:184143</a>]</p> </li> <li id="DGGGTT98"> <p><a class="existingWikiWord" href="/nlab/show/Gianguido+Dall%27Agata">Gianguido Dall'Agata</a>, Davide Fabbri, Christophe Fraser, <a class="existingWikiWord" href="/nlab/show/Pietro+Fr%C3%A9">Pietro Fré</a>, Piet Termonia, <a class="existingWikiWord" href="/nlab/show/Mario+Trigiante">Mario Trigiante</a>, <em>The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>Osp</mi><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">|</mo><mn>4</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">Osp(8|4)</annotation></semantics></math> singleton action from the supermembrane</em>, Nucl. Phys. B <strong>542</strong> (1999) 157-194 [<a href="https://doi.org/10.1016/S0550-3213(98)00765-2">doi:10.1016/S0550-3213(98)00765-2</a>, <a href="http://arxiv.org/abs/hep-th/9807115">arXiv:hep-th/9807115</a>]</p> </li> </ul> <p>with popular exposition in:</p> <ul> <li id="DuffSutton88"><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, Christine Sutton: <em>The Membrane at the End of the Universe</em>, New Scientist <strong>118</strong> (1988) 67-71 [<a href="http://inspirehep.net/record/268230">inspire:268230</a>, ISSN:0028-6664]</li> </ul> <p>Further discussion including also <a class="existingWikiWord" href="/nlab/show/M5-branes">M5-branes</a> and <a class="existingWikiWord" href="/nlab/show/D-branes">D-branes</a>:</p> <ul> <li id="ClausKalloshProeyen97"> <p><a class="existingWikiWord" href="/nlab/show/Piet+Claus">Piet Claus</a>, <a class="existingWikiWord" href="/nlab/show/Renata+Kallosh">Renata Kallosh</a>, <a class="existingWikiWord" href="/nlab/show/Antoine+Van+Proeyen">Antoine Van Proeyen</a>, <em>M 5-brane and superconformal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(0,2)</annotation></semantics></math> tensor multiplet in 6 dimensions</em>, Nucl. Phys. B <strong>518</strong> (1998) 117-150 [<a href="https://doi.org/10.1016/S0550-3213(98)00137-0">doi:10.1016/S0550-3213(98)00137-0</a>, <a href="http://arxiv.org/abs/hep-th/9711161">arXiv:hep-th/9711161</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Piet+Claus">Piet Claus</a>, <a class="existingWikiWord" href="/nlab/show/Renata+Kallosh">Renata Kallosh</a>, J. Kumar, <a class="existingWikiWord" href="/nlab/show/Paul+K.+Townsend">Paul K. Townsend</a>, <a class="existingWikiWord" href="/nlab/show/Antoine+Van+Proeyen">Antoine Van Proeyen</a>, <em>Conformal Theory of M2, D3, M5 and “D1+D5” Branes</em>, JHEP 9806 (1998) 004 [<a href="https://doi.org/10.1088/1126-6708/1998/06/004">doi:10.1088/1126-6708/1998/06/004</a>, <a href="https://arxiv.org/abs/hep-th/9801206">arXiv:hep-th/9801206</a>]</p> </li> <li id="PastiSorokinTonin99"> <p><a class="existingWikiWord" href="/nlab/show/Paolo+Pasti">Paolo Pasti</a>, <a class="existingWikiWord" href="/nlab/show/Dmitri+Sorokin">Dmitri Sorokin</a>, <a class="existingWikiWord" href="/nlab/show/Mario+Tonin">Mario Tonin</a>, <em>Branes in Super-AdS Backgrounds and Superconformal Theories</em>, Proceedings, <em>International Workshop on Supersymmetries and Quantum Symmetries (SQS’99)</em>, Moscow (July 27-31, 1999) [<a href="http://arxiv.org/abs/hep-th/9912076">arXiv:hep-th/9912076</a>, <a href="https://inspirehep.net/literature/511348">inspire:511348</a>]</p> </li> <li> <p>C. Grojean, J. Mourad, <em>Super fivebranes near the boundary of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>AdS</mi> <mn>7</mn></msub><mo>×</mo><msup><mi>S</mi> <mn>4</mn></msup></mrow><annotation encoding="application/x-tex">AdS_7 \times S^4</annotation></semantics></math></em>, Nuclear Physics B <strong>567</strong> 1–2 (2000) 133-150 [<a href="https://doi.org/10.1016/S0550-3213(99)00335-1">doi:10.1016/S0550-3213(99)00335-1</a>, <a href="https://arxiv.org/abs/hep-th/9903164">arXiv:hep-th/9903164</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Alexei+Nurmagambetov">Alexei Nurmagambetov</a>, I. Y. Park <em>On the M5 and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi mathvariant="normal">AdS</mi> <mn>7</mn></msub><mo stretchy="false">/</mo><msub><mi>CFT</mi> <mn>6</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{AdS}_7/CFT_6</annotation></semantics></math> correspondence</em>, Physics Letters B</p> <p><strong>524</strong> 1–2 (2002) 185-191 [<a href="https://doi.org/10.1016/S0370-2693(01)01375-2">doi:10.1016/S0370-2693(01)01375-2</a>, <a href="https://arxiv.org/abs/hep-th/0110192">arXiv:hep-th/0110192</a>]</p> </li> </ul> <p>Review:</p> <ul> <li id="Duff98"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <em>Anti-de Sitter space, branes, singletons, superconformal field theories and all that</em>, Int. J. Mod. Phys. A <strong>14</strong> (1999) 815-844 [<a href="https://doi.org/10.1142/S0217751X99000403">doi:10.1142/S0217751X99000403</a>, <a href="https://arxiv.org/abs/hep-th/9808100">arXiv:hep-th/9808100</a>]</p> </li> <li id="Duff99"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <em>TASI Lectures on Branes, Black Holes and Anti-de Sitter Space</em>, lectures at <em><a href="https://inspirehep.net/conferences/972153">9th CRM Summer School: Theoretical Physics at the End of the 20th Century</a></em> at <a href="https://inspirehep.net/conferences/972127">TASI 99</a> (1999) [<a href="https://arxiv.org/abs/hep-th/9912164">arXiv:hep-th/9912164</a>, <a href="https://inspirehep.net/literature/511822">inspire:511822</a>]</p> </li> </ul> <p>The resulting <a class="existingWikiWord" href="/nlab/show/superconformal+algebra">super-conformal</a> <a class="existingWikiWord" href="/nlab/show/brane+scan">brane scan</a>:</p> <ul> <li id="Duff09"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Near-horizon brane-scan revived</em>, Nucl. Phys. B <strong>810</strong> (2009) 193-209 [<a href="https://doi.org/10.1016/j.nuclphysb.2008.11.001">doi:10.1016/j.nuclphysb.2008.11.001</a>, <a href="http://arxiv.org/abs/0804.3675">arXiv:0804.3675</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>The conformal brane-scan: an update</em>, J. High Energ. Phys. <strong>2022</strong> 54 (2022) [<a href="https://doi.org/10.1007/JHEP06(2022)054">doi:10.1007/JHEP06(2022)054</a>, <a href="https://arxiv.org/abs/2112.13784">arXiv:2112.13784</a>]</p> </li> </ul> <p>Related:</p> <ul> <li>Hironori Mori, Satoshi Yamaguchi, §3 in: <em>M5-branes and Wilson Surfaces in AdS7/CFT6 Correspondence</em>, Phys. Rev. D <strong>90</strong> (2014) 026005 [<a href="https://doi.org/10.1103/PhysRevD.90.026005">doi:10.1103/PhysRevD.90.026005</a>, <a href="https://arxiv.org/abs/1404.0930">arXiv:1404.0930</a>]</li> </ul> <p>Analogous discussion for embeddings with less supersymmetry, corresponding to <a class="existingWikiWord" href="/nlab/show/defect+QFT">defects</a></p> <ul> <li> <p>Nadav Drukker, Simone Giombi, <a class="existingWikiWord" href="/nlab/show/Arkady+A.+Tseytlin">Arkady A. Tseytlin</a>, Xinan Zhou, <em>Defect CFT in the 6d <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(2,0)</annotation></semantics></math> theory from M2 brane dynamics in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>AdS</mi> <mn>7</mn></msub><mo>×</mo><msup><mi>S</mi> <mn>4</mn></msup></mrow><annotation encoding="application/x-tex">AdS_7 \times S^4</annotation></semantics></math></em>, J. High Energ. Phys. <strong>2020</strong> 101 (2020) [<a href="https://doi.org/10.1007/JHEP07(2020)101">doi:10.1007/JHEP07(2020)101</a>, <a href="https://arxiv.org/abs/2004.04562">arXiv:2004.04562</a>]</p> </li> <li> <p>Varun Gupta, <em>Holographic M5 branes in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi mathvariant="normal">AdS</mi> <mn>7</mn></msub><mo>×</mo><msup><mi>S</mi> <mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{AdS}_7 \times S^4</annotation></semantics></math></em>, J. High Energ. Phys. <strong>2021</strong> 32 (2021) [<a href="https://doi.org/10.1007/JHEP12(2021)032">doi:10.1007/JHEP12(2021)032</a>, <a href="https://arxiv.org/abs/2109.08551">arXiv:2109.08551</a>]</p> </li> <li> <p>Varun Gupta, <em>More Holographic M5 branes in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi mathvariant="normal">AdS</mi> <mn>7</mn></msub><mo>×</mo><msup><mi>S</mi> <mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{AdS}_7 \times S^4</annotation></semantics></math></em>, Phys. Lett. B <strong>853</strong> (2024) 138650 [<a href="https://doi.org/10.1016/j.physletb.2024.138650">doi:10.1016/j.physletb.2024.138650</a>, <a href="https://arxiv.org/abs/2301.02528">arXiv:2301.02528</a>]</p> </li> </ul> </div></body></html> </div> <div class="revisedby"> <p> Last revised on July 1, 2024 at 13:53:08. 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