Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification

TL;DR

This paper analyzes N=3 supersymmetric Chern-Simons theories with ADE classification, showing their correspondence with affine Dynkin diagrams and computing the partition function for the D_4 case, supporting a conjecture about eigenvalue distributions.

Contribution

It establishes a classification of such theories via affine Dynkin diagrams and computes the D_4 partition function, extending previous A_n results and exploring dualities.

Findings

Theories correspond to affine Dynkin diagrams.

Partition function computed for D_4 quiver.

Partition function invariant under generalized Seiberg duality.

Abstract

We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S^3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A_n series was studied in detail before, in this paper we compute the partition function for the D_4 quiver. The D_4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.