The complete superconformal index for N=6 Chern-Simons theory

TL;DR

This paper computes the superconformal index for N=6 Chern-Simons theory with gauge group U(N) x U(N), using localization, and confirms its agreement with the dual gravity description in AdS_4 x S^7/Z_k at large N.

Contribution

It provides the first comprehensive calculation of the superconformal index for arbitrary Chern-Simons level k in N=6 theories, including monopole operators, and matches it with gravity predictions.

Findings

Index matches supergravity predictions at large N.

Monopole operators are crucial for the index.

Method can be applied to other superconformal theories.

Abstract

We calculate the superconformal index for N=6 Chern-Simons-matter theory with gauge group U(N) X U(N) at arbitrary allowed value of the Chern-Simons level k. The calculation is based on localization of the path integral for the index. Our index counts supersymmetric gauge invariant operators containing inclusions of magnetic monopole operators, where latter operators create magnetic fluxes on 2-sphere. Through analytic and numerical calculations in various sectors, we show that our result perfectly agrees with the index over supersymmetric gravitons in AdS_4 X S^7/Z_k in the large N limit. Monopole operators in nontrivial representations of U(N) X U(N) play important roles. We also comment on possible applications of our methods to other superconformal Chern-Simons theories.