The gravity dual of supersymmetric gauge theories on a squashed three-sphere

TL;DR

This paper constructs a gravity dual for certain three-dimensional supersymmetric gauge theories on a squashed three-sphere, providing an exact check of the gauge/gravity correspondence in a non-conformal setting.

Contribution

It introduces a new supersymmetric gravity solution corresponding to gauge theories on a squashed sphere with background gauge fields, and verifies the duality through partition function calculations.

Findings

Exact agreement of partition functions on both sides of the duality.

First gravity dual for 3D N=2 theories on a squashed sphere with background gauge fields.

Validation of gauge/gravity correspondence beyond conformal theories.

Abstract

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1) x U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern-Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting.