Superconformal Indices for Orbifold Chern-Simons Theories

TL;DR

The authors compute the superconformal indices for three-dimensional ${\cal N}=4$ and ${\cal N}=5$ Chern-Simons-matter theories and compare them to gravity on AdS$_4\times S^7$ orbifolds, focusing on large $N$ and large $k$ limits. They show exact agreement with gravity in the ${\cal N}=5$ case when twisted-sector contributions at orbifold fixed loci are absent, while for ${\cal N}=4$ theories the twisted sector is essential to achieve matching, illustrating a stringy (beyond supergravity) contribution to the index. The analysis extends to the dual ABJM proposal, where partial agreement suggests that twisted sectors or more refined gravity descriptions are necessary for a full match. Overall, the work provides a rigorous cross-check of AdS$_4$/CFT$_3$ for orbifold geometries and demonstrates how twisted sectors encode crucial stringy information in the index.

Abstract

We calculate the superconformal indices of recently discovered three-dimensional N=4,5 Chern-Simons-matter theories and compare them with the corresponding indices of supergravity on AdS4 times orbifolds of S7. We find perfect agreement in the large N and large k limit, provided that the twisted sector contributions at the fixed loci of the orbifolds are properly taken into account. We also discuss the index for the so-called "dual ABJM" proposal.

Figures (1)

• Figure 1: Matter content of (a) $U$-type and (b) $OSp$-type quiver theories.