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

TL;DR

The authors construct a one-parameter family of gravity duals to large-N supersymmetric gauge theories on a squashed five-sphere by solving Euclidean Romans $F(4)$ supergravity in six dimensions and uplifting to massive IIA. They perform holographic renormalization to compute the renormalized on-shell action and show exact agreement with the large-N squashed-sphere partition function and BPS Wilson loop in the dual 5d theory. By analyzing expansions around the boundary and around Euclidean AdS$_6$, they demonstrate how the squashing parameter controls the bulk geometry and match the field theory results up to sixth order in the perturbation. Finally, they propose a conjecture relating the holographic free energy to the data of the Killing vector and isometry parameters, suggesting a universal relation for supersymmetric backgrounds with topology of a six-ball and $U(1)^3$ isometry.

Abstract

We present the gravity dual of large N supersymmetric gauge theories on a squashed five-sphere. The one-parameter family of solutions is constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplifts to massive type IIA supergravity. By renormalizing the theory with appropriate counterterms we evaluate the renormalized on-shell action for the solutions. We also evaluate the large N limit of the gauge theory partition function, and find precise agreement.