AdS$_5$ Holography and Higher-Derivative Supergravity

TL;DR

This paper investigates four-derivative corrections in 5d $ ext{AdS}_5$ supergravity, analyzing their impact on holographic conformal anomalies and black string entropy, with explicit embeddings in string and M-theory.

Contribution

It explicitly constructs supersymmetric four-derivative invariants in 5d supergravity and connects these to holographic anomalies and black string entropy corrections.

Findings

Derived explicit four-derivative supergravity action in Poincaré frame.

Linked higher-derivative terms to corrections in conformal anomalies.

Calculated entropy corrections for supersymmetric black strings.

Abstract

We study four-derivative corrections to 5d $\mathcal{N}=2$ minimal gauged supergravity using tools from conformal supergravity. There are two supersymmetric invariants at the four-derivative order and we show explicitly how to write down the action in the Poincar\'{e} frame in terms of their coefficients. We apply our results in the context of holography where the four-derivative terms in the supergravity action translate into corrections to the conformal anomalies of the dual 4d $\mathcal{N}=1$ SCFT. We use these results to study corrections to the entropy of the supersymmetric black string solutions of minimal supergravity. We also discuss explicit embeddings of the 5d supergravity in string and M-theory and use them to fix the higher-derivative coefficients in terms of the microscopic parameters.