Non-topological logarithmic corrections in minimal gauged supergravity

TL;DR

This paper calculates the logarithmic entropy corrections for AdS4 black holes in minimal gauged supergravity, revealing non-topological contributions and implications for quantum degrees of freedom and UV completion.

Contribution

It demonstrates that logarithmic corrections in AdS differ from flat space, showing non-topological terms and linking these corrections to the theory's ultraviolet properties.

Findings

Logarithmic corrections match between near horizon and full geometry up to zero modes.

Supersymmetric black holes in AdS can have non-topological logarithmic corrections.

Microscopic data suggests the full correction is topological, indicating UV completion relevance.

Abstract

We compute the logarithmic correction to the entropy of asymptotically AdS$_4$ black holes in minimal ${\cal N}=2$ gauged supergravity. We show that for extremal black holes the logarithmic correction computed in the near horizon geometry agrees with the result in the full geometry up to zero mode contributions, thus clarifying where the quantum degrees of freedom lie in AdS spacetimes. In contrast to flat space, we observe that the logarithmic correction for supersymmetric black holes can be non-topological in AdS as it is controlled by additional four-derivative terms other than the Euler density. The available microscopic data and results in 11d supergravity indicate that the full logarithmic correction is topological, which suggests that the topological nature of logarithmic corrections could serve as a diagnosis of whether a low-energy gravity theory admits an ultraviolet completion.