Exact results on ABJ theory and the refined topological string

TL;DR

This paper provides exact calculations of the ABJ theory partition function on a three-sphere, revealing its complete determination by the refined topological string on local P^1 x P^1, including membrane instanton effects.

Contribution

It offers the first exact computation of the ABJ partition function for various parameters using the Fermi gas approach, linking it to refined topological string theory.

Findings

Exact ABJ partition functions computed for various parameters.

Partition function fully determined by refined topological string on local P^1 x P^1.

Membrane instanton effects included in the analysis.

Abstract

We study the partition function of the ABJ theory, which is the N=6 superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local P^1 x P^1, including membrane instanton effects in the M-theory dual.