The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

TL;DR

This paper explores matrix models for N=3 supersymmetric Chern-Simons theories, introducing folding techniques to relate different quiver gauge theories and deriving dualities from string theory configurations.

Contribution

It introduces a folding/unfolding method to connect various quiver theories and relates them to string theory brane setups, expanding understanding of their dualities.

Findings

Mapping orthosymplectic to unitary quivers via folding

Deriving non-simply laced quivers from simply laced ones

Relating 3D Seiberg duality to 4D Seiberg duality

Abstract

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.