The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS$_4$ Holography

TL;DR

This paper investigates four-derivative corrections in four-dimensional $ ext{AdS}_4$ supergravity, revealing their universal impact on black hole thermodynamics and holographic partition functions, with solutions unaffected at the equations of motion level.

Contribution

It provides a general formula for the regularized on-shell action incorporating higher-derivative effects in $ ext{AdS}_4$ supergravity, and applies this to holography for precise subleading corrections.

Findings

Higher-derivative corrections are controlled by two real constants.

Solutions of the two-derivative theory are unchanged by these corrections.

Derived explicit subleading corrections for supersymmetric partition functions.

Abstract

We study four-derivative corrections to four-dimensional $\mathcal{N}=2$ minimal gauged supergravity and show that they are controlled by two real constants. The solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. We use this to derive a general formula for the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. We employ our results in the context of holography to derive explicit expressions for the subleading corrections in the large $N$ expansion of supersymmetric partition functions on various compact manifolds for a large class of three-dimensional SCFTs.