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| Supersymmetric Yang–Mills theory | |
|---|---|
| Name | Supersymmetric Yang–Mills theory |
| Field | Theoretical physics |
| Introduced | 1970s |
| Key people | Pierre Fayet, Sergio Ferrara, Bruno Zumino, Edward Witten, Nathan Seiberg |
Supersymmetric Yang–Mills theory is a class of quantum field theories combining Yang–Mills theory gauge dynamics with supersymmetry symmetry relating bosons and fermions, developed in the 1970s by researchers including Pierre Fayet, Bruno Zumino, and Sergio Ferrara. It provides a laboratory for exploring nonperturbative effects studied by Edward Witten and Nathan Seiberg, and it plays a central role in investigations connecting gauge theory and string theory such as the AdS/CFT correspondence and M-theory. These theories serve as prototypes in studies of confinement, duality, anomalies, and moduli spaces that influenced work by researchers affiliated with institutions like Princeton University, Institute for Advanced Study, and CERN.
Supersymmetric Yang–Mills theories generalize Paul Dirac-inspired spinor formulations and Yang–Mills theory gauge symmetry by imposing global supersymmetry generators first systematized in work at places like CERN and SLAC. Early formulations by Pierre Fayet and Bruno Zumino introduced minimal models used later in analyses by Edward Witten and Nathan Seiberg, while applications influenced programs at Harvard University and Stanford University. Theories are classified by gauge group choices such as SU(N), SO(N), and Sp(N), and by the number of supersymmetry charges denoted N=1, N=2, N=4 in four dimensions, a taxonomy used in studies at Caltech and MIT.
The Lagrangian of a four-dimensional N=1 model couples a Yang–Mills gauge field valued in the Lie algebra of groups like SU(N) to a gaugino, a Majorana fermion, with interactions encoded by covariant derivatives familiar from work at CERN and Princeton University. Extended variants N=2 and N=4 add chiral multiplets and adjoint scalars first organized in publications by Sergio Ferrara and Bruno Zumino, with the N=4 model achieving maximal supersymmetry studied by Michael Green and John Schwarz in the context of superstring theory. The action contains kinetic terms, Yukawa couplings, and potential terms constrained by supersymmetry representations classified in textbooks authored by researchers at Cambridge University and Oxford University.
The supersymmetry algebra combines the Poincaré algebra elements studied by Paul Dirac and Eugene Wigner with supercharges whose anticommutators produce translations and central charges explored by Sergio Ferrara and Peter West. Supersymmetry transformations act on fields through spinor parameters, an approach used in constructions by Bruno Zumino and elaborated in lectures at Institute for Advanced Study and Perimeter Institute. Central extensions and BPS bounds were analyzed by Edward Witten and Cumrun Vafa in studies of solitonic objects and spectra tied to work on Bogomolny equations and Seiberg–Witten theory.
Classically, moduli spaces of vacua in N=2 and N=4 theories are parametrized by scalar expectation values breaking gauge groups like SU(N) to Cartan subalgebras, a structure analyzed in seminal papers from Harvard University and Princeton University. Flat directions and Higgs branches connect to concepts studied by Nathan Seiberg and Edward Witten in analyses that invoke singularities similar to those examined in ADE classification literature associated with researchers at Institute of Theoretical Physics. Classical Coulomb branches, Higgs branches, and mixed branches are organized by complex geometry techniques used in collaborations involving Shing-Tung Yau and Philip Candelas.
Quantum corrections modify coupling running and anomalous dimensions; the beta function of N=1 theories was computed in approaches influenced by work at CERN and SLAC, while the exact vanishing of the beta function in N=4 was emphasized by Michael Green and John Schwarz in studies related to superstring theory. Anomalies such as the chiral anomaly and trace anomaly were examined by Alberto Sirlin-style techniques and by researchers at MIT and Caltech, informing constraints on low-energy effective actions used in analyses by Nathan Seiberg and Edward Witten. Holomorphy and nonrenormalization theorems constraining superpotentials were formulated by Seiberg and others, paralleling methods taught in seminars at Princeton University and Harvard University.
Nonperturbative dynamics include confinement, instantons, monopoles, and Seiberg–Witten duality; instanton calculus roots trace to work by Alexander Belavin, Victor Zakharov, and others, while monopole solutions relate to the work of Gerard 't Hooft and Alexander Polyakov. Seiberg and Edward Witten derived exact low-energy effective actions for N=2 theories using holomorphicity and duality arguments that influenced studies at Harvard University and Rutgers University. S-duality and electric-magnetic duality in N=4 theories were explored by Ashoke Sen and linked to analyses in AdS/CFT correspondence research at Institute for Advanced Study and CERN.
Supersymmetric Yang–Mills theories appear on worldvolumes of D-branes analyzed by Joseph Polchinski in Type II string theory and provide field theory duals in the AdS/CFT correspondence developed by Juan Maldacena, connecting Anti-de Sitter space with conformal field theories studied at Princeton University and Harvard University. Studies of matrix models and M-theory by Tom Banks and collaborators relate N=4 SYM to nonperturbative formulations pursued at SLAC and Perimeter Institute. Applications extend to model-building in phenomenology by groups at CERN and Fermilab, and to mathematical developments in geometric representation theory connected to work by Edward Witten and Anton Kapustin.