Patch-wise equivariant localization in 5d gauged supergravity

Abstract: I will discuss a novel approach for obtaining the Euclidean on-shell action of a large class of known (and still to be found) solutions of 5d gauged supergravity. The geometries in question include multi-center solutions: black holes, black rings, black lenses, topological solitons, …. In the ungauged limit results match known on-shell actions of explicit flat space muli-center geometries. I will discuss the localization procedure including subtleties concerning holographic renormalization, and dealing with the non-trivial topology of the gauge fields due to CS terms in 5d. Finally, I will mention intriguing relations to various “volumes” found in the equivariant localization literature.