On Supersymmetric Gauge Theories on S^4 x S^1

TL;DR

This paper constructs supersymmetric gauge theories on the five-dimensional space S^4 x S^1, explores their supersymmetry transformations, and applies localization to compute their partition functions, revealing differences from four-dimensional theories.

Contribution

It develops a consistent supersymmetric gauge theory framework on S^4 x S^1 and connects it to known 4D N=2 theories via dimensional reduction.

Findings

Supersymmetry transformations compatible with S^4 x S^1 geometry are found.

No standard Yang-Mills action exists in five dimensions except in the 4D limit.

Localization technique is successfully applied to compute partition functions.

Abstract

We construct supersymmetric gauge theory on S^4 x S^1. We find a consistent supersymmetry transformations which reduced to the 4D N=2 supersymmetry transformation studied by Pestun by the dimensional reduction on S^1. We find there is no analogue of the usual Yang-Mills action except in the 4D limit. We also apply the localization technique to the partition function of the theories.