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

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/L-2 with a topologically non-trivial background gauge field. This metric is of Eguchi-Elanson-AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S-2 cycle. (C) 2012 Elsevier B.V. All rights reserved.