Superconformal Indices for ${\cal N}=6$ Chern Simons Theories

TL;DR

This paper computes the superconformal index of a specific ${ m N}=6$ Chern-Simons theory and confirms its agreement with the dual gravity description in the large N and large k limit.

Contribution

It provides the first one-loop field theory calculation of the superconformal index for this class of theories and verifies the AdS/CFT correspondence at the quantum level.

Findings

Superconformal index matches between field theory and gravity in the large N, large k limit.

First one-loop computation of the superconformal index for ${ m N}=6$ Chern-Simons theories.

Confirms the duality proposed by Aharony et al. at the quantum level.

Abstract

Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we perform the one loop computation that determines the field theory superconformal index of this theory and compare with the index computed over the Fock space of dual supersymmetric gravitons. In the appropriate limit (large $N$ and large $k$) we find a perfect match.