Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2 \times S^1$

TL;DR

This paper solves saddle point equations for large N Chern-Simons matter theories on S^2 x S^1 across multiple phases, confirming dualities and providing exact free energy calculations at all temperatures.

Contribution

It provides exact solutions for saddle point equations in three phases of large N Chern-Simons matter theories, extending previous low-temperature results and confirming dualities.

Findings

Exact solutions for saddle point equations in multiple phases.

Explicit free energy calculations at all temperature ranges.

Confirmation of level-rank bosonization dualities.

Abstract

It has been recently demonstrated that the thermal partition function of any large $N$ Chern-Simons gauge theories on $S^2$, coupled to fundamental matter, reduces to a capped unitary matrix model. The matrix models corresponding to several specific matter Chern-Simons theories at temperature $T$ were determined in arXiv:1301.6169. The large $N$ saddle point equations for these theories were determined in the same paper, and were solved in the low temperature phase. In this paper we find exact solutions for these saddle point equations in three other phases of these theories and thereby explicitly determine the free energy of the corresponding theories at all values of $T^2/N$. As anticipated on general grounds in arXiv:1301.6169, our results are in perfect agreement with conjectured level rank type bosonization dualities between pairs of such theories.