Editing Edward Witten (section)

===Other work===
{{stack|[[File:Gross Witten Hawking TIFR 2001.jpg|thumb|Edward Witten (center) with [[David Gross]] and [[Stephen Hawking]] at [[Strings (conference)|Strings 2001]] at TIFR in  Mumbai, India]]}}

Another of Witten's contributions to physics was to the result of gauge/gravity duality. In 1997, [[Juan Maldacena]] formulated a result known as the [[AdS/CFT correspondence]], which establishes a relationship between certain [[quantum field theories]] and theories of [[quantum gravity]].<ref name="largeN">{{cite journal | author=Juan M. Maldacena | title=The Large N limit of superconformal field theories and supergravity | journal=[[Advances in Theoretical and Mathematical Physics]] | volume=2 | year=1998 | issue=2 | pages=231–252 | arxiv=hep-th/9711200|bibcode = 1998AdTMP...2..231M | doi=10.4310/ATMP.1998.V2.N2.A1 }}</ref> Maldacena's discovery has dominated high-energy theoretical physics for the past 15 years because of its applications to theoretical problems in quantum gravity and quantum field theory. Witten's foundational work following Maldacena's result has shed light on this relationship.<ref>{{cite journal | author=Edward Witten | title=Anti-de Sitter space and holography | journal=[[Advances in Theoretical and Mathematical Physics]] | volume=2 | issue=2 | year=1998 | pages=253–291 | arxiv=hep-th/9802150|bibcode = 1998AdTMP...2..253W | doi=10.4310/ATMP.1998.v2.n2.a2 | s2cid=10882387 }}</ref>

In collaboration with [[Nathan Seiberg]], Witten established several powerful results in quantum field theories. In their paper on string theory and [[noncommutative geometry]], Seiberg and Witten studied certain [[noncommutative quantum field theory|noncommutative quantum field theories]] that arise as limits of string theory.<ref>{{cite journal |last1=Seiberg |first1=Nathan |last2=Witten |first2=Edward |year=1999 |title=String Theory and Noncommutative Geometry |journal=[[Journal of High Energy Physics]] |volume=1999 | doi = 10.1088/1126-6708/1999/09/032 | page=032 | issue = 9|arxiv = hep-th/9908142 |bibcode = 1999JHEP...09..032S |s2cid=668885 }}</ref> In another well-known paper, they studied aspects of [[supersymmetric gauge theory]].<ref>{{cite journal |last1=Seiberg |first1=Nathan |last2=Witten |first2=Edward |year=1994 |title=Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory |journal=[[Nuclear Physics B]] |volume=426 |issue=1 |pages=19–52 |arxiv = hep-th/9407087 |bibcode = 1994NuPhB.426...19S |doi = 10.1016/0550-3213(94)90124-4 |s2cid=14361074 }}</ref> The latter paper, combined with Witten's earlier work on topological quantum field theory,<ref name="tqft" /> led to developments in the topology of [[smooth manifold|smooth]] [[4-manifold]]s, in particular the notion of [[Seiberg–Witten invariant]]s.<ref>{{citation|last=Donaldson|first= Simon K. |author-link=Simon Donaldson |title=The Seiberg-Witten equations and 4-manifold topology. |journal=[[Bulletin of the American Mathematical Society]]| series=(N.S.)  |volume=33  |year=1996|issue= 1|pages= 45–70|doi=10.1090/S0273-0979-96-00625-8 |mr=1339810|doi-access=free}}</ref>

With [[Anton Kapustin]], Witten has made deep mathematical connections between S-duality of gauge theories and the [[geometric Langlands correspondence]].<ref>{{cite journal|last1=Kapustin|first1=Anton|last2=Witten|first2=Edward|date=April 21, 2006|title=Electric-Magnetic Duality And The Geometric Langlands Program|journal=Communications in Number Theory and Physics|volume=1|pages=1–236|arxiv=hep-th/0604151|bibcode=2007CNTP....1....1K|doi=10.4310/CNTP.2007.v1.n1.a1|s2cid=30505126}}</ref> Partly in collaboration with Seiberg, one of his recent interests includes aspects of field theoretical description of topological phases in condensed matter and non-supersymmetric dualities in field theories that, among other things, are of high relevance in condensed matter theory. In 2016, he has also brought tensor models to the relevance of holographic and quantum gravity theories, by using them as a generalization of the [[Sachdev–Ye–Kitaev model]].<ref>{{cite journal|last=Witten|first=Edward|date=October 31, 2016|title=An SYK-Like Model Without Disorder|journal=Journal of Physics A: Mathematical and Theoretical|volume=52|issue=47|pages=474002|arxiv=1610.09758
|doi=10.1088/1751-8121/ab3752|s2cid=118412962}}</ref>

Witten has published influential and insightful work in many aspects of quantum field theories and mathematical physics, including the physics and mathematics of anomalies, integrability, dualities, localization, and homologies. Many of his results have deeply influenced areas in theoretical physics (often well beyond the original context of his results), including string theory, quantum gravity and topological condensed matter.<ref name="Stiftung 2023 Witten">{{cite web | last=Stiftung | first=Joachim Herz | title=News | website=Joachim Herz Stiftung | date=2023-07-03 | url=https://www.joachim-herz-stiftung.de/en/about-us/news/edward-witten | access-date=2024-02-25}}</ref> In particular, Witten is known for collaborating with [[Ruth Britto]] on a method calculating scattering amplitudes known as the [[BCFW recursion|BCFW recursion relations]].