Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit

TL;DR

This paper analyzes matrix models from U(N) Chern-Simons matter theories on three spheres, solving beyond the planar limit and including 1/N corrections, to better understand their free energy and non-perturbative effects.

Contribution

It provides a general solution for matrix models with 1/N corrections up to order 1/N^2, extending previous results and applying to complex N=2 theories.

Findings

Reproduces exact free energy results for pure Chern-Simons theory

Solves matrix models with 1/N corrections beyond the planar limit

Applies to N=2 theories with arbitrary matter content

Abstract

A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In particular we study a case where the matrix model potential has 1/N correction and give a general solution thereof up to the order of 1/N^2. We confirm that the general solution correctly reproduces the past exact result of the free energy up to the order in the case of pure Chern-Simons theory. We also apply to the matrix model of N=2 Chern-Simons theory with arbitrary numbers of fundamental chiral multiplets and anti-fundamental ones, which does not admit the Fermi gas analysis in general.