Exact ABJM Partition Function from TBA

TL;DR

This paper computes the exact S^3 partition function of ABJM theory for specific parameters, revealing a polynomial structure and enabling precise determination of membrane instanton corrections.

Contribution

It provides the first exact polynomial expression for the ABJM partition function at various N and k, and determines membrane instanton coefficients numerically.

Findings

Partition function expressed as a polynomial in π^{-1} with rational coefficients.

Exact values of the partition function for N=1 to 19 at k=1.

Numerical determination of membrane 1-instanton correction coefficient.

Abstract

We report on the exact computation of the S^3 partition function of U(N)_k\times U(N)_{-k} ABJM theory for k=1, N=1,...,19. The result is a polynomial in \pi^{-1} with rational coefficients. As an application of our results we numerically determine the coefficient of the membrane 1-instanton correction to the partition function.