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

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.

17 pages; v2: title modified, footnotes 2 and 4 added, other minor changes, reference [9] added

References in corpus (4)

• N=2 supersymmetric theories on squashed three-sphere
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality

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