The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere

TL;DR

This paper constructs gravity duals for three-dimensional N=2 supersymmetric gauge theories on a deformed three-sphere with two parameters, revealing two solution types with distinct free energy behaviors and proposing a related partition function conjecture.

Contribution

It introduces new supersymmetric backgrounds with a two-parameter deformation and finds their gravity duals, expanding the understanding of holography for deformed geometries.

Findings

Two types of gravity solutions with different free energy behaviors.

A conjecture for the localized partition function on these backgrounds.

Identification of complex free energy in one solution type.

Abstract

We present rigid supersymmetric backgrounds for three-dimensional N=2 supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant deformed three-sphere, and their gravity duals. These are described by supersymmetric solutions of four-dimensional N=2 gauged supergravity with a self-dual metric on the ball and different instantons for the graviphoton field. We find two types of solutions, distinguished by their holographic free energies. In one type the holographic free energy is constant, whereas in another type it depends in a simple way on the parameters and is generically complex. This leads to a conjecture for the localized partition function of a class of N=2 supersymmetric gauge theories on these backgrounds.