5d and 6d Supersymmetric Gauge Theories: Prepotentials from Integrable Systems

TL;DR

This paper explores 5d and 6d supersymmetric gauge theories with compactified dimensions, deriving explicit formulas for their prepotentials using integrable systems, and highlighting their perturbative structures.

Contribution

It provides explicit formulas for the perturbative prepotentials of 5d and 6d supersymmetric gauge theories within the integrable systems framework, including matter hypermultiplets.

Findings

Derived explicit formulas for perturbative prepotentials.

Connected supersymmetric gauge theories with integrable systems.

Analyzed theories with matter hypermultiplets in fundamental representations.

Abstract

We discuss $5d$ and $6d$ supersymmetric gauge theories in the target-space with compactified directions and with the matter hypermultiplets in fundamental representations in the framework of integrable systems. In particular, we consider the prepotentials of these theories and derive explicit formulas for their perturbative parts.