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| N=4 SYM | |
|---|---|
| Name | N=4 supersymmetric Yang–Mills theory |
| Field | Theoretical physics |
| Introduced | 1976 |
| Founder | Nathalie Seiberg; others: Edward Witten, Sergio Ferrara, Bruno Zumino |
| Related | AdS/CFT correspondence, Montonen–Olive duality, Super Yang–Mills theory |
N=4 SYM
N=4 SYM is a four-dimensional quantum field theory notable for maximal supersymmetry in four dimensions and exact conformal invariance. It plays a central role in modern theoretical physics through connections to Edward Witten, Juan Maldacena, Seiberg–Witten theory, Alexander Polyakov, Gerard 't Hooft, Nikolai Bogoliubov, Stanley Mandelstam, Leonard Susskind and institutions such as Institute for Advanced Study, CERN, Perimeter Institute, Caltech, Princeton University.
N=4 SYM was constructed in the 1970s and refined in the 1980s by researchers including Sergio Ferrara, Bruno Zumino, Peter West, Lars Brink, John Schwarz, Michael Green and subsequently developed in contexts involving Philip Candelas and Cumrun Vafa. It is studied at places like Harvard University, Massachusetts Institute of Technology, Stanford University, University of Cambridge, and is central to programs led by Nima Arkani-Hamed, Edward Witten, Juan Maldacena, Dimitri Polyakov and collaborators. The theory arises as the worldvolume theory of D3-branes in Joseph Polchinski's string theory framework and was instrumental in formulating the AdS/CFT correspondence by Juan Maldacena with input from Leonard Susskind, Gerasimov and others.
The field content comprises a gauge field, four Majorana (or two Weyl) fermions, and six real scalars transforming in the adjoint representation of a gauge group such as SU(N), SO(N), or USp(2N). The minimal Lagrangian was written down by Brink, Schwarz and Scherk and improved in superspace form by Sergio Ferrara and Bruno Zumino, following algebraic methods introduced by P. Ramond and Victor Kac. The action is invariant under global R-symmetry SU(4)_R which was analyzed by Murray Gell-Mann and used in later classifications by Dixon and Ferrara. Quantization techniques build on work of Ken Wilson, Gerard 't Hooft, Kenneth G. Wilson, Murray Gell-Mann and renormalization methods developed by Steven Weinberg and Kenneth Wilson.
The symmetry algebra is the superconformal algebra PSU(2,2|4) studied by Nahm and classified via methods used by Eugene Wigner and Emil Artin in representation theory. Supersymmetry generators, conformal generators, and R-symmetry generators close into this algebra; systematic representation theory techniques were advanced by Joseph Bernstein, Israel Gelfand, Harish-Chandra and modernized in contexts by David Kazhdan and Alexander Beilinson. Local and global symmetry structures relate to techniques by Michael Peskin, Ian Affleck, Elliott Lieb and modular methods influenced by John Conway and Simon Donaldson in related mathematical settings.
The classical moduli space of vacua is the space of gauge-equivalence classes of commuting scalar expectation values, described algebraically by invariant polynomials studied by Emmy Noether and David Hilbert. The Coulomb branch and Higgs branch structure was elucidated in analyses by Seiberg and Edward Witten drawing on methods from Paul Dirac, Andrei Linde and geometric frameworks developed at Institute for Advanced Study and Max Planck Institute. Moduli stabilization and vacuum counting connect to results by Cumrun Vafa, Shamit Kachru, Savas Dimopoulos and techniques from Michael Atiyah and Isadore Singer.
Perturbatively N=4 SYM is finite with vanishing beta function, a result derived using diagrammatic methods by Gerard 't Hooft, M.S. Grisaru, Curtis Callan and confirmed via superspace by Sergio Ferrara. Nonperturbative sectors include instantons analyzed by A.A. Belavin, Alexander Polyakov, A.M. Polyakov, A.S. Schwarz and treated with localization techniques introduced by Nikita Nekrasov and extended by Vasily Pestun. Montonen–Olive duality proposals by Clifford Montonen and David Olive and analyses by Edward Witten and Seiberg illuminate S-duality and strong–weak coupling maps using techniques developed by Ken Intriligator and Nathan Seiberg.
N=4 SYM is central to the AdS/CFT correspondence conjectured by Juan Maldacena relating SU(N) gauge theory to type IIB string theory on AdS5×S5, a duality explored by Gubser, Klebanov, Polyakov, Igor Klebanov, Stephen Hawking and elaborated in holography programs at Harvard, Princeton, Caltech and Perimeter Institute. Integrability in the planar limit was developed by Nikita Beisert, Matthias Staudacher, Ludwig Faddeev and Vladimir Korepin connecting to spin chains studied by Hans Bethe and algebraic Bethe ansatz methods by R.J. Baxter.
N=4 SYM has produced insights across topology and geometry via links to Donaldson theory, Seiberg–Witten invariants, Mirror symmetry by Philip Candelas and Paul Aspinwall, representation theory via the geometric Langlands program championed by Edward Witten and Dennis Gaitsgory, and number-theoretic structures examined by Andrew Wiles and Richard Taylor. It informs scattering amplitude techniques developed by Zvi Bern, Lance Dixon, David Kosower, Nima Arkani-Hamed and Freddy Cachazo and has motivated computational advances at CERN, SLAC, DESY and Los Alamos National Laboratory. Connections extend to quantum information and condensed matter programs led by John Preskill, Subir Sachdev, Patrick Lee and to mathematical frameworks advanced by Maxim Kontsevich, Simon Donaldson and Michael Atiyah.
Category:Supersymmetric quantum field theories