A Note on the Partition Function of ABJM theory on S^3

TL;DR

This paper analyzes the partition function of ABJM theory on S^3, revealing a difference in behavior for even and odd k, with implications for AdS/CFT correspondence.

Contribution

It provides an exact evaluation of the partition function for N=2 and highlights the k-dependence difference between even and odd k values.

Findings

Exact eigenvalue integral evaluation for N=2

Different Z dependence on k for even and odd k

Implications for AdS/CFT correspondence

Abstract

We study the partition function Z of U(N)_k x U(N)_{-k} Chern-Simons matter theory (ABJM theory) on S^3 which is recently obtained by the localization method. We evaluate the eigenvalue integral in Z exactly for the N=2 case. We find that Z has a different dependence on k for even k and odd k. We comment on the possible implication of this result in the context of AdS/CFT correspondence.