The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere

Understand

We present rigid supersymmetric backgrounds for three-dimensional N=2 supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant deformed three-sphere, and their gravity duals.

• These are described by supersymmetric solutions of four-dimensional N=2 gauged supergravity with a self-dual metric on the ball and different instantons for the graviphoton field.
• We find two types of solutions, distinguished by their holographic free energies.
• In one type the holographic free energy is constant, whereas in another type it depends in a simple way on the parameters and is generically complex.