Gravity duals of supersymmetric gauge theories on three-manifolds

We study gravity duals to a broad class of $$ mathcal{n} $$ = 2 supersymmetric gauge theories defined on a general class of three-manifold geometries. the gravity backgrounds are based on euclidean self-dual solutions to four-dimensional gauged supergravity. as well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric killing vector, finding a simple closed formula when the solution has u(1) × u(1) symmetry. our result agrees with the large n limit of the free energy of the dual gauge theory, computed using localization. this constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large n limit, defined on a general class of background three-manifold geometries.