A Systematic Study on Matrix Models for Chern-Simons-matter Theories

TL;DR

This paper systematically analyzes matrix models from Chern-Simons-matter theories, revealing bounded eigenvalue distributions and Wilson loop vevs at large couplings, differing from ABJM theory, with explicit solutions for certain gauge groups.

Contribution

It provides a systematic method to solve planar matrix models for Chern-Simons-matter theories and relates solutions to Fuchsian systems, highlighting bounded eigenvalue distributions.

Findings

Eigenvalue distributions are confined in bounded regions at large couplings.

Wilson loop vevs remain bounded even as 't Hooft couplings grow large.

Explicit resolvent solutions are obtained for theories with U(N)×U(N) gauge groups.

Abstract

We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the 't Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling limit. This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.