One-loop determinants for black holes in 4d gauged supergravity

Abstract

We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d $\mathcal{N}=2$ gauged supergravity, initiated in [1803.05920]. The emphasis here is on the missing steps in the previous localization analysis, mainly dealing with one-loop determinants for abelian vector multiplets and hypermultiplets on the non-compact space ${\mathbb{H}}_2\times \hat{I}{\pounds }_{\mathrm{g}}$ with particular boundary conditions. We use several different techniques to arrive at consistent results, which have a most direct bearing on the logarithmic correction terms to the Bekenstein-Hawking entropy of said black holes.

44 pages; v2 fixes the source for displaying eq. (1.1)