CINXE.COM

<!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> Michael Duff 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[/*></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[//><!]]> </script> <script type="text/javascript"> <![CDATA[//><!]]> </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> Michael Duff </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/10846/#Item_3" 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 style="float:right;margin:-30px 0px 00px 20px;"> <img src="https://grahamfarmelo.com/wp-content/uploads/2019/07/Mike-Portrait-28_900.jpg" width="180" /> </div> <p><br /></p> <p>Michael Duff is professor of theoretical physics at Imperial College London. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thickmathspace"></mspace><mspace width="thickmathspace"></mspace></mrow><annotation encoding="application/x-tex">\;\;</annotation></semantics></math></p> <p>He made foundational contributions to <a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a> and <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a>. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thickmathspace"></mspace><mspace width="thickmathspace"></mspace></mrow><annotation encoding="application/x-tex">\;\;</annotation></semantics></math></p> <ul> <li> <p><a href="http://michaelduff.weebly.com">personal webpage</a></p> </li> <li> <p><a href="http://www.imperial.ac.uk/AP/faces/pages/read/Home.jsp?person=m.duff&_adf.ctrl-state=6bq6bx4cv_3&_afrRedirect=2848555508000">institute webpage</a></p> </li> <li> <p><a href="http://en.wikipedia.org/wiki/Michael_Duff">Wikipedia entry</a></p> </li> </ul> <p>Autobiographical notes around encountering <a class="existingWikiWord" href="/nlab/show/Chris+Isham">Chris Isham</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Chris Isham: mentor, colleague, friend</em> (<a href="https://arxiv.org/abs/2112.13722">arXiv:2112.13722</a>)</li> </ul> <p>See also:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Leron+Borsten">Leron Borsten</a>, <a class="existingWikiWord" href="/nlab/show/Alessio+Marrani">Alessio Marrani</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+N.+Pope">Christopher N. Pope</a>, <a class="existingWikiWord" href="/nlab/show/Kellogg+Stelle">Kellogg Stelle</a>, <em>Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday</em>, Proceedings of the Royal Society A, <p><strong>478</strong> (2022) 2259 [<a href="https://doi.org/10.1098/rspa.2022.0166">doi:10.1098/rspa.2022.0166</a>]</p> </li> </ul> <p><br /></p> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#students'>Students</a></li> <li><a href='#intervies'>Intervies</a></li> <li><a href='#Quotes'>Quotes</a></li> <li><a href='#selected_writings'>Selected writings</a></li> </ul> </div> <h2 id="students">Students</h2> <p>Among Duff’s former students is <a class="existingWikiWord" href="/nlab/show/Hisham+Sati">Hisham Sati</a>.</p> <p><br /></p> <h2 id="intervies">Intervies</h2> <ul> <li> <p>Interview by Graham Fermelo, <em>The universe speaks in numbers – Interview 14</em> (<a href="https://grahamfarmelo.com/the-universe-speaks-in-numbers-interview-14/">web</a>)</p> </li> <li> <p>Interview by <a class="existingWikiWord" href="/nlab/show/Hisham+Sati">Hisham Sati</a>, <a class="existingWikiWord" href="/nlab/show/Urs+Schreiber">Urs Schreiber</a>, at <em><a class="existingWikiWord" href="/nlab/show/M-Theory+and+Mathematics">M-Theory and Mathematics</a></em> 2020:</p> <p>see: <em><a class="existingWikiWord" href="/nlab/show/Duff+interview+at+M-Theory-Mathematics+2020">Duff interview at M-Theory-Mathematics 2020</a></em></p> </li> </ul> <h2 id="Quotes">Quotes</h2> <p>On the open problem of formulating <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a>:</p> <p><br /></p> <p><a href="#Duff96">Duff 96, totality of Section 6</a>:</p> <blockquote> <p>The overriding problem in superunification in the coming years will be to take the Mystery out of M-theory, while keeping the Magic and the Membranes.</p> </blockquote> <p><br /></p> <p><a href="#Duff98">Duff 98a, last paragraph (p. 6)</a>:</p> <blockquote> <p>Despite all these successes, physicists are glimpsing only small corners of M-theory; the big picture is still lacking.</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[...]</annotation></semantics></math></p> <p>Indeed future historians may judge the late 20th century as a time when theorists were like children playing on the seashore, diverting themselves with the smoother pebbles or prettier shells of superstrings while the great ocean of M-theory lay undiscovered before them.</p> </blockquote> <p><br /></p> <p><a href="#Duff98b">Duff 98b, p. 6</a>:</p> <blockquote> <p>we are only just beginning to scratch the surface of the ultimate meaning of M-theory, and for the time being therefore, M stands for Magic and Mystery too.</p> </blockquote> <p><br /></p> <p><a href="#Duff99">Duff 99, p.330</a>:</p> <blockquote> <p>future historians may judge the period 1984-95 as a time when theorists were like boys playing by the sea shore, and diverting themselves with the smoother pebbles or prettier shells of perturbative ten-dimensiorial superstrings while the great ocean of non-perturbative eleven-dimensional M-theory lay all undiscovered before them.</p> </blockquote> <p><br /></p> <p>Interview with <a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a> by Graham Fermelo, <em>The universe speaks in numbers – Interview 14</em> (<a href="https://grahamfarmelo.com/the-universe-speaks-in-numbers-interview-14/">web</a>):</p> <blockquote> <p id="WeDontKnowWhatItIs"> (17:04) The problem we face is that we have a patchwork understanding of M-theory, like a quilt. We understand this corner and that corner, but what’s lacking is the overarching big picture. So directly or indirectly, my research hopes to explain what M-theory really is. We don’t know what it is.</p> <p>In a certain sense, and this is not a popular statement, I think it’s premature to be asking: “What are the empirical consequences”, because it’s not yet in a mature enough state, where we can sensibly make falsifiable prediction.</p> </blockquote> <p><br /></p> <p id="Duff20"> <a class="existingWikiWord" href="/nlab/show/Duff+interview+at+M-Theory-Mathematics+2020">Duff interview at M-Theory-Mathematics 2020</a>:</p> <blockquote> <p>(06:59) But the matrix model itself was not all of M-theory; it was a corner of M-theory, and it told us certain interesting things, but there were interesting things about M-theory that it didn’t tell us.</p> <p>(07:13) I think we are still looking, in fact, for what M-theory really is.</p> <p>(07:19) We have a patchwork picture. We understand various corners. But the overarching big picture of M-theory is still waiting to be discovered, in my view.</p> <p>(08:12) M-theory in 1995 was very promising, and it’s taught us a lot about the fundamental interactions; but the final theory is still not with us.</p> <p>(12:46) I wouldn’t like to predict what the ultimate picture of M-theory will be; I imagine it will be something quite different from what we can imagine now.</p> <p>(16:36) That’s why I think M-theory is not yet in a mature enough stage for us to make falsifiable predictions.</p> <p>(16:44) We don’t understand the theory sufficiently well yet to do so.</p> </blockquote> <h2 id="selected_writings">Selected writings</h2> <p>On <a class="existingWikiWord" href="/nlab/show/KK-compactification">KK-compactification</a> of <a class="existingWikiWord" href="/nlab/show/11-dimensional+supergravity">11-dimensional supergravity</a> on a <a class="existingWikiWord" href="/nlab/show/squashed+sphere">squashed</a> <a class="existingWikiWord" href="/nlab/show/7-sphere">7-sphere</a> with <a class="existingWikiWord" href="/nlab/show/G%E2%82%82-holonomy">G₂-holonomy</a> (<a class="existingWikiWord" href="/nlab/show/M-theory+on+G%E2%82%82-manifolds">M-theory on G₂-manifolds</a>):</p> <ul> <li id="AwadaDuffPope83"> <p><a class="existingWikiWord" href="/nlab/show/Moustafa+A.+Awada">Moustafa A. Awada</a>, <a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <em><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>N</mi><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">N=8</annotation></semantics></math> Supergravity Breaks Down to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">N=1</annotation></semantics></math></em>, Phys. Rev. Lett. <strong>50</strong> 5 (1983) 294-297 [<a href="https://doi.org/10.1103/PhysRevLett.50.294">doi:10.1103/PhysRevLett.50.294</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <a class="existingWikiWord" href="/nlab/show/Bengt+Nilsson">Bengt Nilsson</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <em>Spontaneous Supersymmetry Breaking by the Squashed Seven-Sphere</em>, Phys. Rev. Lett. 50, 2043 (1983) (<a href="https://doi.org/10.1103/PhysRevLett.50.2043">doi:10.1103/PhysRevLett.50.2043</a>, <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.846">erratum</a>)</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/double+dimensional+reduction">double dimensional reduction</a> of the <a class="existingWikiWord" href="/nlab/show/super-membrane">super-membrane</a> (the <a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a>) to the <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+superstring">Green-Schwarz superstring</a>:</p> <ul> <li id="DuffHoweInamiStelle87"><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Paul+Howe">Paul Howe</a>, T. Inami, <a class="existingWikiWord" href="/nlab/show/Kellogg+Stelle">Kellogg Stelle</a>, <em>Superstrings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>D</mi><mo>=</mo><mn>10</mn></mrow><annotation encoding="application/x-tex">D=10</annotation></semantics></math> from Supermembranes in <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></em>, Phys. Lett. B191 (1987) 70 and in <a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a> (ed.) <em><a class="existingWikiWord" href="/nlab/show/The+World+in+Eleven+Dimensions">The World in Eleven Dimensions</a></em> 205-206 (1987) (<a href="http://inspirehep.net/record/245249">spire</a>)</li> </ul> <p>On the emergence of <a class="existingWikiWord" href="/nlab/show/superconformal+field+theory">superconformal field theory</a> in the perturbations of the <a class="existingWikiWord" href="/nlab/show/super-membrane">super-membrane</a> <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+sigma+model">Green-Schwarz sigma model</a> around a classical solution stretched along the <a class="existingWikiWord" href="/nlab/show/asymptotic+boundary">asymptotic boundary</a> of <a class="existingWikiWord" href="/nlab/show/anti+de+Sitter+spacetime">anti de Sitter spacetime</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="DuffSutton88"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, C. Sutton, <em>The Membrane at the End of the Universe</em>, New Sci. 118 (1988) 67-71 (<a href="http://inspirehep.net/record/268230?ln=en">spire:268230</a>)</p> </li> </ul> <p>predating the modern formulation of the <a class="existingWikiWord" href="/nlab/show/AdS-CFT+correspondence">AdS-CFT correspondence</a>, amplified in</p> <ul> <li id="Duff98"><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. A14:815-844, 1999 (<a href="https://arxiv.org/abs/hep-th/9808100">arXiv:hep-th/9808100</a>)</li> </ul> <p>On the corresponding <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+sigma-model">brane scan</a> of <a class="existingWikiWord" href="/nlab/show/super-conformal+algebra">super-conformal</a> branes:</p> <ul> <li> <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://cds.cern.ch/record/184143">cds:184143</a>, <a href="http://dx.doi.org/10.1016/0370-2693(88)90544-8">doi:10.1016/0370-2693(88)90544-8</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Near-horizon brane-scan revived</em>, Nucl. Phys. B 810:193-209 2009 (<a href="http://arxiv.org/abs/0804.3675">arXiv:0804.3675</a>)</p> </li> <li id="Duff21"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>The conformal brane-scan: an update</em> (<a href="https://arxiv.org/abs/2112.13784">arXiv:2112.13784</a>)</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/quantization">quantization</a> of the <a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a> <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+sigma-model">Green-Schwarz sigma-model</a>:</p> <ul> <li id="DuffInamiPopeSezginStelle88"><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, T. Inami, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <a class="existingWikiWord" href="/nlab/show/Ergin+Sezgin">Ergin Sezgin</a>, <a class="existingWikiWord" href="/nlab/show/Kellogg+Stelle">Kellogg Stelle</a>, <em>Semiclassical Quantization of the Supermembrane</em>, Nucl.Phys. B297 (1988) 515-538 (<a href="http://inspirehep.net/record/247064">spire:247064</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+compactification">Kaluza-Klein compactification</a></p> <ul> <li id="Duff94"><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Kaluza-Klein Theory in Perspective</em>, Proc. of the Symposium: <em>The Oskar Klein Centenary</em>, World Scientific, Singapore (1994) [<a href="http://arxiv.org/abs/hep-th/9410046">arXiv:hep-th/9410046</a>, <a href="https://doi.org/10.1142/2816">doi:10.1142/2816</a>]</li> </ul> <p>and specifically in <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>:</p> <ul> <li id="DuffNilssonPope86"> <p><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <a class="existingWikiWord" href="/nlab/show/Bengt+Nilsson">Bengt Nilsson</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>, <em>Kaluza-Klein supergravity</em>, Physics Reports Volume 130, Issues 1–2, January 1986, Pages 1-142 (<a href="https://inspirehep.net/record/229417">spire:229417</a>, <a href="https://doi.org/10.1016/0370-1573(86)90163-8">doi:10.1016/0370-1573(86)90163-8</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Bengt+Nilsson">Bengt Nilsson</a>, <a class="existingWikiWord" href="/nlab/show/Christopher+Pope">Christopher Pope</a>: <em>Kaluza-Klein Supergravity 2025</em>, in: <em>Half a Century of Supergravity</em> [<a href="https://arxiv.org/abs/2502.07710">arXiv:2502.07710</a>]</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/black+brane">black</a> <a class="existingWikiWord" href="/nlab/show/M2-brane">M2-brane</a>-solutions to <a class="existingWikiWord" href="/nlab/show/D%3D11+supergravity">D=11 supergravity</a>:</p> <ul> <li id="DuffStelle91"><a class="existingWikiWord" href="/nlab/show/Mike+Duff">Mike Duff</a>, <a class="existingWikiWord" href="/nlab/show/Kellogg+Stelle">Kellogg Stelle</a>, <em>Multi-membrane 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</em>, Phys. Lett. B 253, 113 (1991) (<a href="http://inspirehep.net/record/299386">spire:299386</a>, <a href="https://doi.org/10.1016/0370-2693(91)91371-2">doi:10.1016/0370-2693(91)91371-2</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/black+branes">black branes</a> and <a class="existingWikiWord" href="/nlab/show/solitonic+branes">solitonic branes</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>]</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> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a>:</p> <ul> <li id="Duff96"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>M-Theory (the Theory Formerly Known as Strings)</em>, Int. J. Mod. Phys. A11 (1996) 5623-5642 (<a href="http://arxiv.org/abs/hep-th/9608117">arXiv:hep-th/9608117</a>)</p> </li> <li id="Duff98"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>The Theory Formerly Known as Strings</em>, Scientific American 1998 (<a href="https://www.nikhef.nl/pub/services/biblio/bib_KR/sciam14395569.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/DuffFormerlyStrings98.pdf" title="pdf">pdf</a>)</p> </li> <li id="Duff98b"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>A Layman’s Guide to M-theory</em>, Abdus Salam Memorial Meeting, Trieste, Italy, 19 - 22 Nov 1997, pp.184-213 (<a href="https://arxiv.org/abs/hep-th/9805177">arXiv:hep-th/9805177</a>, <a href="https://cds.cern.ch/record/355721">cds:355721</a>)</p> </li> <li id="Duff99"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em><a class="existingWikiWord" href="/nlab/show/The+World+in+Eleven+Dimensions">The World in Eleven Dimensions</a></em> (1999)</p> </li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/brane+scan">brane scan</a> which classifies 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>-<a class="existingWikiWord" href="/nlab/show/brane">brane</a> <a class="existingWikiWord" href="/nlab/show/sigma-models">sigma-models</a> given by <a class="existingWikiWord" href="/nlab/show/Green-Schwarz+action+functionals">Green-Schwarz action functionals</a>:</p> <ul> <li id="Duff87"><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>Supermembranes: the first fifteen weeks</em>, Class. Quant. Grav. 5 (1988) 189 (<a href="https://doi.org/10.1088/0264-9381/5/1/023">doi:10.1088/0264-9381/5/1/023</a>, <a href="https://inspirehep.net/record/248034">spire:248034</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/string-string+duality">string-string duality</a>:</p> <ul> <li id="DuffKhuri93"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Ramzi+Khuri">Ramzi Khuri</a>, <em>Four-Dimensional String/String Duality</em>, Nucl.Phys. B411 (1994) 473-486 (<a href="https://arxiv.org/abs/hep-th/9305142">arXiv:hep-th/9305142</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Ruben+Minasian">Ruben Minasian</a>, <em>Putting string/string duality to the test</em>, Nucl.Phys. B436 (1995) 507-528 (<a href="https://arxiv.org/abs/hep-th/9406198">arXiv:hep-th/9406198</a>)</p> </li> </ul> <p>and specifically on the <a class="existingWikiWord" href="/nlab/show/I8">I8</a>-term:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/James+Liu">James Liu</a>, <a class="existingWikiWord" href="/nlab/show/Ruben+Minasian">Ruben Minasian</a>, <em>Eleven Dimensional Origin of String/String Duality: A One Loop Test</em>, Nucl.Phys. B452 (1995) 261-282 (<a href="https://arxiv.org/abs/hep-th/9506126">arXiv:hep-th/9506126</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>:</p> <ul> <li id="Duff04"><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <em>The status of local supersymmetry</em>, in: <em>From Quarks to Black Holes: Progress in understanding the logic of Nature</em>, World Scientific (2005) 60-116 [<a href="http://arxiv.org/abs/hep-th/0403160">arXiv:hep-th/0403160</a>, <a href="https://doi.org/10.1142/9789812701794_0004">doi:10.1142/9789812701794_0004</a>]</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/Freudenthal+magic+square">magic squares</a> of <a class="existingWikiWord" href="/nlab/show/magic+supergravities">magic supergravities</a> and <a class="existingWikiWord" href="/nlab/show/U-duality">U-duality</a> via the <a class="existingWikiWord" href="/nlab/show/classical+double+copy">classical double copy</a>:</p> <ul> <li id="BorstenDuffHughesNagy13"> <p><a class="existingWikiWord" href="/nlab/show/Leron+Borsten">Leron Borsten</a>, <a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Mia+J.+Hughes">Mia J. Hughes</a>, <a class="existingWikiWord" href="/nlab/show/Silvia+Nagy">Silvia Nagy</a>, <em>A magic square from Yang-Mills squared</em>, Phys. Rev. Lett. <strong>112</strong> (2014) 131601 [<a href="http://arxiv.org/abs/1301.4176">arXiv:1301.4176</a>]</p> </li> <li id="ABDHN"> <p><a class="existingWikiWord" href="/nlab/show/Alexandros+Anastasiou">Alexandros Anastasiou</a>, <a class="existingWikiWord" href="/nlab/show/Leron+Borsten">Leron Borsten</a>, <a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>, <a class="existingWikiWord" href="/nlab/show/Mia+J.+Hughes">Mia J. Hughes</a>, <a class="existingWikiWord" href="/nlab/show/Silvia+Nagy">Silvia Nagy</a>, <em>A magic pyramid of supergravities</em>, JHEP (2014) 178 [<a href="http://arxiv.org/abs/1312.6523">arXiv:1312.6523</a>]</p> </li> </ul> <p>On the early history of the notion of <em><a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a></em>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Duff">Michael Duff</a>: <em>M-history without the M</em>, Contemporary Physics <strong>57</strong> 1 (2016) [<a href="http://arxiv.org/abs/1501.04098">arXiv:1501.04098</a>, <a href="https://doi.org/10.1080/00107514.2014.992964">doi:10.1080/00107514.2014.992964</a>]</li> </ul> <div class="property">category: <a class="category_link" href="/nlab/all_pages/people">people</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on February 13, 2025 at 02:28:26. See the <a href="/nlab/history/Michael+Duff" 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/Michael+Duff" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussion/10846/#Item_3">Discuss</a><span class="backintime"><a href="/nlab/revision/Michael+Duff/35" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/Michael+Duff" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/Michael+Duff" accesskey="S" class="navlink" id="history" rel="nofollow">History (35 revisions)</a> <a href="/nlab/show/Michael+Duff/cite" style="color: black">Cite</a> <a href="/nlab/print/Michael+Duff" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/Michael+Duff" id="view_source" rel="nofollow">Source</a> </div> </div>  </div>  </body> </html>