5D SYM on 3D Deformed Spheres

TL;DR

This paper explores the relationship between superconformal indices of class S theories and 5D N=2 supersymmetric Yang-Mills theory on deformed three-spheres, using localization techniques to compute partition functions.

Contribution

It formulates 5D N=2 SYM on deformed three-spheres with preserved supersymmetry and clarifies issues related to partial twisting on Riemann surfaces, extending previous work.

Findings

Partition functions computed on squashed and ellipsoid three-spheres.

Clarification of partial twisting effects in superconformal index calculations.

Extension of localization techniques to deformed three-sphere backgrounds.

Abstract

We reconsider the relation of superconformal indices of superconformal field theories of class S with five-dimensional N=2 supersymmetric Yang-Mills theory compactified on the product space of a round three-sphere and a Riemann surface. We formulate the five-dimensional theory in supersymmetric backgrounds preseving N=2 and N=1 supersymmetries and discuss a subtle point in the previous paper concerned with the partial twisting on the Riemann surface. We further compute the partition function by localization of the five-dimensional theory on a squashed three-sphere in N=2 and N=1 supersymmetric backgrounds and on an ellipsoid three-sphere in an N=1 supersymmetric background.