Matrix models for 2* theories

Abstract

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the adjoint representation. We consider theories in four, five and six dimensions, and obtain new matrix models respectively of rational, trigonometric and elliptic type. The matrix models for five- and six-dimensional U(1) theories are derived from the topological vertex construction related to curves of genus one and two.