N=2 supersymmetric theories on squashed three-sphere

TL;DR

This paper studies how deforming a 3d N=2 supersymmetric theory on a squashed sphere affects its partition function, revealing a dependence on the squashing parameter and analyzing large N behavior.

Contribution

It introduces a squashing deformation preserving supersymmetry and computes the resulting partition function, highlighting how it varies with the squashing parameter and large N limit.

Findings

Partition function depends non-trivially on squashing parameter

Large N free energy scales as N^{3/2} and is modified by squashing

Deformation preserves all four supercharges and SU(2)_L x U(1)_r symmetry

Abstract

We investigate a squashing deformation of 3d N=2 supersymmetric theories on three-sphere, which have four supercharges. The deformation preserves SU(2)_L x U(1)_r isometry and all four supersymmetries. We compute the partition function and find non-trivial dependence on the squashing parameter. We also consider the large N limit of a certain class of quiver gauge theories which have free energy of order N^{3/2}, and show that the free energy on the squashed sphere differs from that on round sphere by a certain factor depending only on the squashing parameter.