Abstract
We construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) x U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere, and we find a one-parameter family of 3/4 BPS deformations and a two-parameter family of (generically) 1/4 BPS deformations. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplift to massive type IIA supergravity. We holographically renormalize the Romans theory, and use our general result to compute the renormalized on-shell actions for the solutions. The results agree perfectly with the large N limit of the dual gauge theory partition function, which we compute using large N matrix model techniques. In addition we compute BPS Wilson loops in these backgrounds, both in supergravity and in the large N matrix model, again finding precise agreement. Finally, we conjecture a general formula for the partition function on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector.
Highlights
Over the last few years there has been increasing interest in defining and studying supersymmetric gauge theories on curved backgrounds
These five-sphere backgrounds are continuously connected to the round sphere, and we find a one-parameter family of 3/4 BPS deformations and a two-parameter family of 1/4 BPS deformations
The result for the perturbative partition function (2.25) in the previous section is valid for a general supersymmetric gauge theory in five dimensions, but we focus on a particular class of theories with gauge group G = USp(2N ), that arises from a system of N D4-branes and some number of D8-branes and orientifold planes in massive type IIA string theory
Summary
Over the last few years there has been increasing interest in defining and studying supersymmetric gauge theories on curved backgrounds. In this paper we shall present the first construction of gravity duals to gauge theories on non-conformally flat backgrounds (certain families of squashed fivespheres). Having constructed supergravity solutions that have squashed five-sphere conformal boundaries, we compute the holographic free energy F = − log Z by holographically renormalizing the on-shell Euclidean action. Another exact observable that can be computed both in supersymmetric gauge theories and in supergravity are Wilson loops, which are the subject of section 7. We include appendices A, B and C, which expand upon some of the elements in the main body of the paper
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