Supersymmetric Index In Four-Dimensional Gauge Theories

By E. Witten. 2000

138 citations recorded by the source corpus.

This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements that probe confinement and oblique confinement and the possible spontaneous breaking of chiral symmetry and of global symmetries, such as charge conjugation, that are derived from outer automorphisms of the gauge group. Predictions for the index and its refinements are obtained on the basis of standard hypotheses about the infrared behavior of gauge theories. The predictions are confirmed via microscopic calculations which involve a Born-Oppenheimer computation of the spectrum as well as mathematical formulas involving triples of commuting elements of G and the Chern-Simons invariants of flat bundles on the three-torus.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ef42ece736e3a63936f1c8ffaa45dbfc00008e2d

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In Nuclear and High Energy Physics

1. N. Seiberg
2. E. Witten
3. C. Vafa
4. Yuji Tachikawa
5. Clay Córdova
6. Marcos Mariño
7. F. Benini
8. D. Gaiotto

Citations in the corpus

• Triples, Fluxes, and Strings (2001, background): “This insight was crucial in resolving some puzzles about counting vacua in four-dimensional gauge theory [17,20-25].”
• M-Theory Dynamics On A Manifold Of G_2 Holonomy (2001, background): “As proved in [68] (in accord with conjectures in [64]), the values of the Chern-Simons invariants for flat bundles with a given t are 2πμ t , (6.”
• Anomalies in the space of coupling constants and their dynamical applications II (2019, methodology): “Following [43], we will determine the relation between the fractional instantons and the background gauge fields B by evaluating the instanton number on a specific G{ZpGq bundle.”
• Reading between the lines of four-dimensional gauge theories (2013, methodology): “We can also repeat the same discussion in the Hamiltonian formalism of [44], putting the theory on some spatial 3-manifold Y .”
• Topology of character varieties of Abelian groups (2013, background): “The description of the space of commuting elements in a compact Lie group is an interesting algebro-geometric problem with applications in mathematical physics, remarkably in supersymmetric Yang-Mills theory and mirror symmetry ([7, 28, 47, 48]).”