Matrix models for 2* theories

TL;DR

This paper develops matrix model representations for 2* theories, including 4D, 5D, and 6D cases, revealing new rational, trigonometric, and elliptic models derived from topological string techniques.

Contribution

It introduces a novel method to express 2* theories' partition functions as matrix models across multiple dimensions, connecting to topological vertex constructions.

Findings

Derived matrix models for 4D, 5D, and 6D 2* theories.

Connected matrix models to topological string theory.

Provided explicit forms of rational, trigonometric, and elliptic models.

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.