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

Understand

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.