Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity

TL;DR

This paper studies how higher derivative supersymmetric terms affect BPS black hole attractors and entropy in 4d gauged supergravity, revealing corrections that connect to microscopic dual descriptions and various asymptotic geometries.

Contribution

It derives the impact of Weyl-squared terms on BPS black hole entropy and attractors in gauged supergravity, extending previous two-derivative results to include higher derivative corrections.

Findings

Higher derivative terms modify BPS black hole entropy.

Explicit examples for different asymptotics are provided.

Weyl-squared terms alter relations in ungauged supergravity.

Abstract

We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (or other Riemann surface) preserves half of the supercharges in $N=2$ supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending on the model, the attractors are part of full black hole solutions with different asymptotics, such as Minkowski, AdS$_4$, and hvLif$_4$. We give explicit examples for each of the asymptotic cases and comment on the implications. Among other results, we find that the Weyl-squared terms spoil the exact two-derivative relation to non-BPS asymptotically flat black holes in ungauged supergravity.