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

TL;DR

This paper constructs a gravity dual for 3D N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, matching holographic free energy with large N localized partition functions and exploring related solutions with non-trivial topology.

Contribution

It provides explicit 1/2 BPS Euclidean supergravity solutions with non-trivial gauge fields that serve as gravity duals for supersymmetric gauge theories on squashed spheres.

Findings

Holographic free energy matches large N partition functions.

Constructed Taub-NUT-AdS and Eguchi-Hanson-AdS type solutions.

Demonstrated non-trivial topology effects in gravity duals.

Abstract

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub-NUT-AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern-Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S^3/Z_2 with a topologically non-trivial background gauge field. This metric is of Eguchi-Hanson-AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S^2 cycle.