Toric gravitational instantons in gauged supergravity

We introduce a general class of toric gravitational instantons in D=4, N=2 gauged supergravity, namely Euclidean supersymmetric solutions with U(1)2 isometry. Such solutions are specified by a “supergravity labeled polytope,” where the labels encode the four-manifold topology, the choice of magnetic fluxes, and certain signs associated with the Killing spinor. Equivariant localization allows us to write down the gravitational free energy for such a solution, assuming it exists, and study its properties. These results open the way for a systematic study of holography in this setting, where the dual large N field theories are defined on the boundary three-manifolds, which are (squashed) lens spaces L(p,q) or generalizations with orbifold singularities. Published by the American Physical Society 2025