Edward Witten

Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton.^[4] Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics.^[5] In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals.^[6] He is considered the practical founder of M-theory.^[7]

Edward Witten
Witten in 2008
Born	(1951-08-26) August 26, 1951 (age 71) Baltimore, Maryland, U.S.
Citizenship	American
Education	Brandeis University (BA) Princeton University (MA, PhD)
Known for	M-theory Seiberg–Witten theory Seiberg–Witten map Seiberg–Witten invariants Wess–Zumino–Witten model Weinberg–Witten theorem Gromov–Witten invariant Hořava–Witten domain wall Vafa–Witten theorem Witten index BCFW recursion Topological quantum field theory (Witten-type TQFTs) Topological string theory CSW rules Witten conjecture Witten zeta function Hanany–Witten transition Twistor string theory Chern–Simons theory Positive energy theorem Witten–Veneziano mechanism
Spouse	Chiara Nappi
Children	3
Awards	MacArthur Fellowship (1982) Albert Einstein Medal (1985) Dirac Medal (1985) Alan T. Waterman Award (1986) Fields Medal (1990) Dannie Heineman Prize (1998) Nemmers Prize (2000) National Medal of Science (2002) Harvey Prize (2005) Henri Poincaré Prize (2006) Crafoord Prize (2008) Lorentz Medal (2010) Isaac Newton Medal (2010) Fundamental Physics Prize (2012) Kyoto Prize (2014) Albert Einstein Award (2016)^[1]
Scientific career
Fields	Theoretical physics Mathematical physics Superstring theory
Institutions	Institute for Advanced Study Harvard University Oxford University California Institute of Technology Princeton University
Thesis	Some Problems in the Short Distance Analysis of Gauge Theories (1976)
Doctoral advisor	David Gross^[2]
Other academic advisors	Sidney Coleman^[3] Michael Atiyah^[3]
Doctoral students	Jonathan Bagger (1983) Cumrun Vafa (1985) Xiao-Gang Wen (1987) Dror Bar-Natan (1991) Shamit Kachru (1994) Eva Silverstein (1996) Sergei Gukov (2001)
Website	www.ias.edu/sns/witten

Early life and education

Witten was born on August 26, 1951, in Baltimore, Maryland, to a Jewish family.^[8] He is the son of Lorraine (née Wollach) Witten and Louis Witten, a theoretical physicist specializing in gravitation and general relativity.^[9]

Witten attended the Park School of Baltimore (class of '68), and received his Bachelor of Arts degree with a major in history and minor in linguistics from Brandeis University in 1971.^[10]

He had aspirations in journalism and politics and published articles in both The New Republic and The Nation in the late 1960s.^[11][12] In 1972 he worked for six months on George McGovern's presidential campaign.^[13]

Witten attended the University of Michigan for one semester as an economics graduate student before dropping out.^[14] He returned to academia, enrolling in applied mathematics at Princeton University in 1973, then shifting departments and receiving a PhD in physics in 1976 and completing a dissertation, "Some problems in the short distance analysis of gauge theories", under the supervision of David Gross.^[15] He held a fellowship at Harvard University (1976–77), visited Oxford University (1977–78),^[3][16] was a junior fellow in the Harvard Society of Fellows (1977–1980), and held a MacArthur Foundation fellowship (1982).^[4]

Research

Fields medal work

Witten was awarded the Fields Medal by the International Mathematical Union in 1990.^[17]

In a written address to the ICM, Michael Atiyah said of Witten:^[5]

Although he is definitely a physicist (as his list of publications clearly shows) his command of mathematics is rivaled by few mathematicians, and his ability to interpret physical ideas in mathematical form is quite unique. Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems ... He has made a profound impact on contemporary mathematics. In his hands physics is once again providing a rich source of inspiration and insight in mathematics.^[5]

 

Edward Witten (left) with mathematician Shigefumi Mori, probably at the ICM in 1990, where they received the Fields Medal.

As an example of Witten's work in pure mathematics, Atiyah cites his application of techniques from quantum field theory to the mathematical subject of low-dimensional topology. In the late 1980s, Witten coined the term topological quantum field theory for a certain type of physical theory in which the expectation values of observable quantities encode information about the topology of spacetime.^[18] In particular, Witten realized that a physical theory now called Chern–Simons theory could provide a framework for understanding the mathematical theory of knots and 3-manifolds.^[19] Although Witten's work was based on the mathematically ill-defined notion of a Feynman path integral and therefore not mathematically rigorous, mathematicians were able to systematically develop Witten's ideas, leading to the theory of Reshetikhin–Turaev invariants.^[20]

Another result for which Witten was awarded the Fields Medal was his proof in 1981 of the positive energy theorem in general relativity.^[21] This theorem asserts that (under appropriate assumptions) the total energy of a gravitating system is always positive and can be zero only if the geometry of spacetime is that of flat Minkowski space. It establishes Minkowski space as a stable ground state of the gravitational field. While the original proof of this result due to Richard Schoen and Shing-Tung Yau used variational methods,^[22][23] Witten's proof used ideas from supergravity theory to simplify the argument.^{[citation needed]}

A third area mentioned in Atiyah's address is Witten's work relating supersymmetry and Morse theory,^[24] a branch of mathematics that studies the topology of manifolds using the concept of a differentiable function. Witten's work gave a physical proof of a classical result, the Morse inequalities, by interpreting the theory in terms of supersymmetric quantum mechanics.^{[citation needed]}

M-theory

By the mid 1990s, physicists working on string theory had developed five different consistent versions of the theory. These versions are known as type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E₈×E₈). The thinking was that of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low-energy limit matched the physics observed in our world today.^{[citation needed]}

Speaking at the string theory conference at University of Southern California in 1995, Witten made the surprising suggestion that these five string theories were in fact not distinct theories, but different limits of a single theory, which he called M-theory.^[25][26] Witten's proposal was based on the observation that the five string theories can be mapped to one another by certain rules called dualities and are identified by these dualities. It led to a flurry of work now known as the second superstring revolution.^{[citation needed]}

Other work

 

Edward Witten (center) with David Gross and Stephen Hawking at 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.^[27] 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.^[28]

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 theories that arise as limits of string theory.^[29] In another well-known paper, they studied aspects of supersymmetric gauge theory.^[30] The latter paper, combined with Witten's earlier work on topological quantum field theory,^[18] led to developments in the topology of smooth 4-manifolds, in particular the notion of Seiberg–Witten invariants.^[31]

With Anton Kapustin, Witten has made deep mathematical connections between S-duality of gauge theories and the geometric Langlands correspondence.^[32] Partly in collaboration with Seiberg, one of his recent interests include 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.^[33]

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.^{[citation needed]}

Awards and honors

Witten has been honored with numerous awards including a MacArthur Grant (1982), the Fields Medal (1990), the Golden Plate Award of the American Academy of Achievement (1997),^[34] the Nemmers Prize in Mathematics (2000), the National Medal of Science^[35] (2002), Pythagoras Award^[36] (2005), the Henri Poincaré Prize (2006), the Crafoord Prize (2008), the Lorentz Medal (2010) the Isaac Newton Medal (2010) and the Fundamental Physics Prize (2012). Since 1999, he has been a Foreign Member of the Royal Society (London), and in March 2016 was elected an Honorary Fellow of the Royal Society of Edinburgh.^[37][38] Pope Benedict XVI appointed Witten as a member of the Pontifical Academy of Sciences (2006). He also appeared in the list of Time magazine's 100 most influential people of 2004. In 2012 he became a fellow of the American Mathematical Society.^[39] Witten was elected as a member of the American Academy of Arts and Sciences in 1984, a member of the National Academy of Sciences in 1988, and a member of the American Philosophical Society in 1993.^[40][41][42] In May 2022 he was awarded an honorary Doctor of Sciences from the University of Pennsylvania.^[43]

In an informal poll at a 1990 cosmology conference, Witten received the largest number of mentions as "the smartest living physicist".^[44]

Personal life

Witten has been married to Chiara Nappi, a professor of physics at Princeton University, since 1979.^[45] They have two daughters and a son. Their daughter Ilana B. Witten is a neuroscientist at Princeton University,^[46] and daughter Daniela Witten is a biostatistician at the University of Washington.^[47]

Witten sits on the board of directors of Americans for Peace Now and on the advisory council of J Street.^[48] He supports the two-state solution and advocates a boycott of Israeli institutions and economic activity beyond its 1967 borders, though not of Israel itself.^[49]

Selected publications

• Some Problems in the Short Distance Analysis of Gauge Theories. Princeton University, 1976. (Dissertation.)
• Roman Jackiw, David Gross, Sam B. Treiman, Edward Witten, Bruno Zumino. Current Algebra and Anomalies: A Set of Lecture Notes and Papers. World Scientific, 1985.
• Green, M., John H. Schwarz, and E. Witten. Superstring Theory. Vol. 1, Introduction. Cambridge Monographs on Mathematical Physics. Cambridge, UK: Cambridge University Press, 1988. ISBN 978-0-521-35752-4.
• Green, M., John H. Schwarz, and E. Witten. Superstring Theory. Vol. 2, Loop Amplitudes, Anomalies and Phenomenology. Cambridge, UK: Cambridge University Press, 1988. ISBN 978-0-521-35753-1.
• Quantum fields and strings: a course for mathematicians. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison and Edward Witten. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1999. Vol. 1: xxii+723 pp.; Vol. 2: pp. i–xxiv and 727–1501. ISBN 0-8218-1198-3, 81–06 (81T30 81Txx).

References

1. . World Cultural Council. June 6, 2016. Archived from the original on June 7, 2016. Retrieved June 6, 2016.
2. Woit, Peter (2006). Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law. New York: Basic Books. p. 105. ISBN 0-465-09275-6.
3. (PDF). Archived from the original (PDF) on August 23, 2016. Retrieved October 30, 2016.
4. "Edward Witten". Institute for Advanced Study. December 9, 2019. Retrieved July 14, 2022.
5. Atiyah, Michael (1990). (PDF). Proceedings of the International Congress of Mathematicians. pp. 31–35. Archived from the original (PDF) on March 1, 2017.
6. Michael Atiyah. (PDF). Mathunion.org. Archived from the original (PDF) on March 1, 2017. Retrieved March 31, 2017.
7. Duff 1998, p. 65
8. Witten biography - MacTutor History of Mathematics
9. The International Who's Who 1992-93, p. 1754.
10. "Edward Witten (1951)". www.nsf.gov. Retrieved August 25, 2020.
11. Witten, Edward (October 18, 1969). "Are You Listening, D.H. Lawrence?". The New Republic.
12. Witten, Edward (December 16, 1968). "The New Left". The Nation.
13. Farmelo, Graham (May 2, 2019). "'The Universe Speaks in Numbers' – Interview 5". Graham Farmelo. from the original on May 3, 2019. Retrieved August 25, 2020. Alt URL
14. Physics, American Institute of (February 24, 2022). "Edward Witten". www.aip.org. Retrieved June 21, 2022.
15. Witten, E. (1976). Some problems in the short distance analysis of gauge theories.
16. Interview by Hirosi Ooguri, Notices of the American Mathematical Society, May 2015, pp. 491–506.
17. (PDF). 2011. Archived from the original (PDF) on February 4, 2012. Retrieved April 13, 2021.
18. Witten, Edward (1988), "Topological quantum field theory", Communications in Mathematical Physics, 117 (3): 353–386, Bibcode:1988CMaPh.117..353W, doi:10.1007/BF01223371, S2CID 43230714
19. Witten, Edward (1989). "Quantum Field Theory and the Jones Polynomial" (PDF). Communications in Mathematical Physics. 121 (3): 351–399. Bibcode:1989CMaPh.121..351W. doi:10.1007/BF01217730. S2CID 14951363.
20. Reshetikhin, Nicolai; Turaev, Vladimir (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". Inventiones Mathematicae. 103 (1): 547–597. Bibcode:1991InMat.103..547R. doi:10.1007/BF01239527. S2CID 123376541.
21. Witten, Edward (1981). "A new proof of the positive energy theorem". Communications in Mathematical Physics. 80 (3): 381–402. Bibcode:1981CMaPh..80..381W. doi:10.1007/BF01208277. S2CID 1035111.
22. Schoen, Robert; Yau, Shing-Tung (1979). "On the proof of the positive mass conjecture in general relativity". Communications in Mathematical Physics. 65 (1): 45. Bibcode:1979CMaPh..65...45S. doi:10.1007/BF01940959. S2CID 54217085.
23. Schoen, Robert; Yau, Shing-Tung (1981). "Proof of the positive mass theorem. II". Communications in Mathematical Physics. 79 (2): 231. Bibcode:1981CMaPh..79..231S. doi:10.1007/BF01942062. S2CID 59473203.
24. Witten, Edward (1982). "Super-symmetry and Morse Theory". Journal of Differential Geometry. 17 (4): 661–692. doi:10.4310/jdg/1214437492.
25. University of Southern California, Los Angeles, Future Perspectives in String Theory, March 13–18, 1995, E. Witten: Some problems of strong and weak coupling
26. Witten, Edward (1995). "String theory dynamics in various dimensions". Nuclear Physics B. 443 (1): 85–126. arXiv:hep-th/9503124. Bibcode:1995NuPhB.443...85W. doi:10.1016/0550-3213(95)00158-O. S2CID 16790997.
27. Juan M. Maldacena (1998). "The Large N limit of superconformal field theories and supergravity". Advances in Theoretical and Mathematical Physics. 2 (2): 231–252. arXiv:hep-th/9711200. Bibcode:1998AdTMP...2..231M. doi:10.4310/ATMP.1998.V2.N2.A1.
28. Edward Witten (1998). "Anti-de Sitter space and holography". Advances in Theoretical and Mathematical Physics. 2 (2): 253–291. arXiv:hep-th/9802150. Bibcode:1998AdTMP...2..253W. doi:10.4310/ATMP.1998.v2.n2.a2. S2CID 10882387.
29. Seiberg, Nathan; Witten, Edward (1999). "String Theory and Noncommutative Geometry". Journal of High Energy Physics. 1999 (9): 032. arXiv:hep-th/9908142. Bibcode:1999JHEP...09..032S. doi:10.1088/1126-6708/1999/09/032. S2CID 668885.
30. Seiberg, Nathan; Witten, Edward (1994). "Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory". Nuclear Physics B. 426 (1): 19–52. arXiv:hep-th/9407087. Bibcode:1994NuPhB.426...19S. doi:10.1016/0550-3213(94)90124-4. S2CID 14361074.
31. Donaldson, Simon K. (1996), "The Seiberg-Witten equations and 4-manifold topology.", Bulletin of the American Mathematical Society, (N.S.), 33 (1): 45–70, doi:10.1090/S0273-0979-96-00625-8, MR 1339810
32. Kapustin, Anton; Witten, Edward (April 21, 2006). "Electric-Magnetic Duality And The Geometric Langlands Program". Communications in Number Theory and Physics. 1: 1–236. arXiv:hep-th/0604151. Bibcode:2007CNTP....1....1K. doi:10.4310/CNTP.2007.v1.n1.a1. S2CID 30505126.
33. Witten, Edward (October 31, 2016). "An SYK-Like Model Without Disorder". Journal of Physics A: Mathematical and Theoretical. 52 (47): 474002. arXiv:1610.09758. doi:10.1088/1751-8121/ab3752. S2CID 118412962.
34. "Golden Plate Awardees of the American Academy of Achievement". www.achievement.org. American Academy of Achievement.
35. "Edward Witten", The President's National Medal of Science: Recipient Details.
36. . Il Crotonese (in Italian). September 23, 2005. Archived from the original on July 22, 2011.
37. "Foreign Members", The Royal Society.
38. . June 21, 2016. Archived from the original on March 9, 2016. Retrieved March 8, 2016.
39. List of Fellows of the American Mathematical Society, retrieved September 1, 2013.
40. "Edward Witten". American Academy of Arts & Sciences. Retrieved May 13, 2020.
41. "Edward Witten". www.nasonline.org. Retrieved May 13, 2020.
42. "APS Member History". search.amphilsoc.org. Retrieved March 21, 2022.
43. "Penn's 2022 Commencement Speaker and Honorary Degree Recipients". Retrieved May 30, 2022.
44. Lemonick, Michael (April 26, 2004). . Time. Archived from the original on September 1, 2006. Retrieved November 1, 2011.
    "At a 1990 conference on cosmology," wrote John Horgan in 2014, "I asked attendees, who included folks like Stephen Hawking, Michael Turner, James Peebles, Alan Guth and Andrei Linde, to nominate the smartest living physicist. Edward Witten got the most votes (with Steven Weinberg the runner-up). Some considered Witten to be in the same league as Einstein and Newton." See "Physics Titan Edward Witten Still Thinks String Theory 'on the Right Track'". scientificamerican.com. September 22, 2014. Retrieved October 14, 2014.
45. Witten, Ed. "The 2014 Kyoto Prize Commemorative Lecture in Basic Sciences" (PDF). Retrieved January 28, 2017.
46. "Faculty » Ilana B. Witten". princeton.edu. Retrieved November 18, 2016.
47. "UW Faculty » Daniela M. Witten". washington.edu. Retrieved July 9, 2015.
48. "Advisory Council". J Street. 2016. Retrieved October 14, 2016.
49. "For an Economic Boycott and Political Nonrecognition of the Israeli Settlements in the Occupied Territories", NYRB, October 2016.

External links

 

Wikimedia Commons has media related to Edward Witten.

 

Wikiquote has quotations related to Edward Witten.

• Faculty webpage
• Publications on ArXiv
• O'Connor, John J.; Robertson, Edmund F., "Edward Witten", MacTutor History of Mathematics archive, University of St Andrews
• Edward Witten at the Mathematics Genealogy Project
• A Physicist's Physicist Ponders the Nature of Reality, Interview with Nathalie Wolchover in Quanta Magazine, November 28, 2017