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| Super Yang–Mills | |
|---|---|
| Name | Super Yang–Mills |
| Field | Theoretical physics |
| Introduced | 1970s |
| Notable | Witten, Seiberg, Maldacena |
Super Yang–Mills Super Yang–Mills is a class of gauge theories combining Gauge theory with Supersymmetry, developed in the 1970s and influential in studies by Edward Witten, Nathan Seiberg, and Juan Maldacena, and used across research at institutions such as Institute for Advanced Study, CERN, and SLAC National Accelerator Laboratory. These theories generalize Yang–Mills theory by pairing gauge bosons with fermionic superpartners and have driven progress in topics connected to Quantum field theory, String theory, and the AdS/CFT correspondence.
Super Yang–Mills models arise from extending Yang–Mills theory with supersymmetry generators introduced in works by Julius Wess, Bruno Zumino, and later developed in contexts involving Gerard 't Hooft, Alexander Polyakov, and Kurt Gödel-adjacent historical discussions, and they underpin modern research at centers like Perimeter Institute and Max Planck Institute for Physics. Theories vary by number of supercharges labeled by N and by gauge group choices such as SU(N), SO(N), and E8 families, and they connect to nonperturbative tools developed by Seiberg and Witten, Seiberg, Witten, and analyses at Harvard University and Princeton University.
The minimal Lagrangian for Super Yang–Mills includes a gauge field A_mu in the adjoint of a gauge group like SU(N) and fermionic gauginos introduced in the Wess–Zumino formulation considered by Julius Wess and Bruno Zumino, with kinetic and interaction terms analogous to those in Yang–Mills theory studied by C. N. Yang and Robert Mills. For N=1 in four dimensions the action couples gauge multiplets and auxiliary fields following constructions used by Steven Weinberg and Michael Peskin, while extended multiplets for N=2 and N=4 were elaborated by researchers at Caltech and MIT and relate to hypermultiplet structures examined by Paul Dirac and Richard Feynman. The field content organizes under representations classified using tools developed by Eugene Wigner and used by Harish-Chandra and Weyl in group theory.
Supersymmetry transformations act on gauge and gaugino fields via spinor charges satisfying an algebra first formalized alongside the Poincaré algebra in works influenced by Yuri Golfand, Evgeny Likhtman, and later reviews by Peter West, and these variations close on translations and gauge transformations as in analyses by Sergio Ferrara and Ali Chamseddine. The on-shell and off-shell formulations exploit auxiliary fields and representations cataloged in texts by Salam and Strathdee and techniques from Noether conserved currents studied by Emmy Noether, with central extensions relevant in studies by Seiberg and Witten when examining BPS bounds and soliton spectra.
Classical solutions include vacuum moduli spaces, instantons, monopoles, and BPS states explored in semiclassical work by Alexander Belavin, Victor Zakharov, Edward Witten, and Nikolai Nekrasov, and the instanton calculus connects to index theorems by Atiyah–Singer and soliton constructions related to Gerard 't Hooft and Alexander Polyakov. Moduli of vacua for N=2 theories were mapped in breakthroughs by Seiberg and Witten using techniques developed at University of Chicago and Princeton University, while classical integrability and self-dual solutions have been studied in contexts associated with Ludwig Faddeev and Lev Lipatov.
Quantum properties include beta functions, anomalies, and nonperturbative dynamics first computed in perturbative series by authors like Curtis Callan and Kenneth Wilson and refined by David Gross and Frank Wilczek. N=1 theories exhibit holomorphy and exact results found using methods by Seiberg and Intriligator, while the vanishing of the beta function in N=4 was noted in analyses by Sven Mandelstam and Howard Georgi; instanton contributions and dualities leverage localization methods due to Nekrasov and the renormalization group frameworks introduced by Kenneth Wilson at CERN and Brookhaven National Laboratory.
Extended supersymmetry for N=2 and N=4 leads to enhanced symmetry and conformal invariance, with N=4 Super Yang–Mills being maximally supersymmetric and conformal as stressed in seminal papers by Maldacena, Gubser, Klebanov, and Witten. N=4 theory with gauge group SU(N) has been central to planar limits and integrability studies by groups at Cornell University and Yale University, and it features S-duality properties explored by Edward Witten and Ashoke Sen with mathematical structures connected to geometric Langlands work by Robert Langlands and Edward Frenkel.
Super Yang–Mills theories, especially N=4 with SU(N), appear on worldvolumes of D-branes in Type IIB string theory and underlie the original AdS/CFT conjecture by Juan Maldacena relating N=4 SYM to Type IIB supergravity on AdS5 × S5, with further developments by Gubser, Klebanov, Polyakov, and Witten and implementations at Institute for Advanced Study and Perimeter Institute. Applications include holographic dualities used by Gerard 't Hooft-inspired large N expansions, black hole microstate counting influenced by Andrew Strominger and Cumrun Vafa, and connections to M-theory researched by groups at Rutgers University and University of Cambridge.