The gravity dual of supersymmetric gauge theories on a squashed $S^1 \times S^3$

Understand

We present a new one-parameter family of supersymmetric solutions deforming AdS_5.

• This is constructed as an asymptotically locally anti de Sitter (AlAdS) solution of five-dimensional minimal gauged supergravity, with topology R x R^4 and a non-trivial graviphoton field, and can be uplifted to ten or eleven dimensional supergravities.
• An analytic continuation of this solution yields the gravity dual to a class of four-dimensional N=1 supersymmetric gauge theories on a curved manifold with topology S^1 x S^3, comprising an SU(2) x U(1)-symmetric squashed three-sphere, with a non-trivial background gauge field coupling to the R-symmetry current.
• We compute the holographically renormalised on-shell action and interpret it in terms of the Casimir energy of the dual field theory.