Localization of superconformal field theory on S1 × S3 and index

A bstract We provide the geometrical meaning of the superconformal index. With this interpretation, the superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a δ ϵ -exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the superconformalindex is expressed.