Five Dimensional Gauge Theories and Relativistic Integrable Systems

TL;DR

This paper presents a non-perturbative solution for five-dimensional N=2 supersymmetric gauge theories on a circle, revealing their connection to relativistic integrable systems and exploring finiteness properties.

Contribution

It introduces a non-perturbative approach to 5D N=2 gauge theories and links them to relativistic integrable systems, highlighting new finiteness features with an adjoint hypermultiplet.

Findings

Pure gauge theory corresponds to known relativistic integrable systems.

The theory with an adjoint hypermultiplet shows finiteness properties.

The inverse radius acts as the speed of light in the integrable systems.

Abstract

We propose a non-perturbative solution of N=2 supersymmetric gauge theory in five dimensions compactified on circle of a radius $R$. We consider the cases of the pure gauge theory as well as the theories with matter in the fundamental and in the adjoint representations. The pure theory as well as the one with adjoint hypermultiplet give rise to the known relativistic integrable systems with ${1\over{R}}$ playing the r\^ole of the speed of light. The theory with adjoint hypermultiplet exhibits some interesting finiteness properties. Talk given at the III International Conference ``Conformal Field Theories and Integrable Models'', Chernogolovka, June 23-30 1996