Seiberg-Witten Theory and Random Partitions

TL;DR

This paper explores the computation of partition functions in N=2 supersymmetric gauge theories using various representations, leading to a rigorous derivation of Seiberg-Witten geometry and extensions to theories with matter and in five dimensions.

Contribution

It introduces new representations for the partition function, such as random partitions and free fermion correlators, enabling rigorous derivation of Seiberg-Witten geometry.

Findings

Derived Seiberg-Witten curves and differentials from statistical models

Extended analysis to theories with matter hypermultiplets

Included five-dimensional compactified theories

Abstract

We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omega-background. The partition function of the theory in the Omega-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, a free fermion correlator. These representations allow to derive rigorously the Seiberg-Witten geometry, the curves, the differentials, and the prepotential. We study pure N=2 theory, as well as the theory with matter hypermultiplets in the fundamental or adjoint representations, and the five dimensional theory compactified on a circle.