The ABCDEF’s of matrix models for supersymmetric Chern-Simons theories

Abstract

We consider $\mathcal{N} = {3}$ 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 ${{\mathbb{Z}}_{{2}}}$ 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.