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

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.

17 pages, corrected typos, references added, published version

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