Supersymmetric Index In Four-Dimensional Gauge Theories

Details Supersymmetric Index In Four-Dimensional Gauge Theories Supersymmetric Index In Four-Dimensional Gauge Theories

2000-06-01

arxiv.org/abs/hep-th/0006010v1

Adv.Theor.Math.Phys.5:841-907,2002

Physics

High Energy Physics

High Energy Physics - Theory

66 pp

Scientific paper

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.

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