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Charging the superconformal index

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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 → ∞. Like the ordinary superconformal index, for N = 4 SYM the charged index is independent of N in the large-N limit.

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Authors and Affiliations

  1. Physics Department, California Institute of Technology, 1200 East California Boulevard, Pasadena, California, 91125, U.S.A

    Benjamin I. Zwiebel

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  1. Benjamin I. Zwiebel
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Correspondence to Benjamin I. Zwiebel.

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ArXiv ePrint: 1111.1773

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Zwiebel, B.I. Charging the superconformal index. J. High Energ. Phys. 2012, 116 (2012). https://doi.org/10.1007/JHEP01(2012)116

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  • DOI: https://doi.org/10.1007/JHEP01(2012)116

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