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

Abstract

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. We also determine the holographic conserved charges of the solution and discuss relations between them.