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 ${\mathbb{H}}_2\times {\Sigma }_{\mathrm{g}}$ 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.

arXiv comment44 pages; v2 fixes the source for displaying eq. (1.1)

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• Universal 3d Cardy Block and Black Hole Entropy
• Rotating Black Hole Entropy from M5-branes
• Large $N$ Partition Functions of the ABJM Theory
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Non-topological logarithmic corrections in minimal gauged supergravity
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• Quantum entropy of BMPV black holes and the topological M-theory conjecture