Charging the Superconformal Index

Abstract

The superconformal index is an important invariant of superconformal field theories. In this note we refine the superconformal index by inserting the charge conjugation operator C. We construct a matrix integral for this charged index for N=4 SYM with SU(N) gauge group. The key ingredient for the construction is a "charged character," which reduces to Tr(C) for singlet representations of the gauge group. For each irreducible real SU(N) representation, we conjecture that this charged character is equal to the standard character for a corresponding representation of SO(N+1) or SP(N-1), for N even or odd respectively. The matrix integral for the charged index passes tests for small N and for N -> infinity. Like the ordinary superconformal index, for N=4 SYM the charged index is independent of N in the large-N limit.

31 pages, v2: minor changes, published version

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Cited by in corpus (12)

• M5-branes from gauge theories on the 5-sphere
• 3d dualities from 4d dualities for orthogonal groups
• Instantons on the 5-sphere and M5-branes
• The supersymmetric index in four dimensions
• The Superconformal Index of Class S Theories of Type D
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• Gauge theories from principally extended disconnected gauge groups
• Discrete gauge theories of charge conjugation
• Vanishing superconformal indices and the chiral symmetry breaking
• Mathematical structures behind supersymmetric dualities
• The Romelsberger Index, Berkooz Deconfinement, and Infinite Families of Seiberg Duals