Black holes in five-dimensional gauged supergravity with higher derivatives

TL;DR

Five-dimensional $\mathcal N=2$ gauged supergravity is studied with higher-derivative $R^2$-type corrections, implemented via supersymmetric completion and integrated to an on-shell action. The authors construct $R$-charged AdS black holes to linear order in the four-derivative parameter $c_2$ and analyze thermodynamics, horizon structure, and entropy. A central result is the holographic relation between $c_2$ and the gauge theory data through anomaly matching, yielding a microscopic expression for the entropy in terms of the CFT central charges $a$ and $c$. This framework connects five-dimensional supergravity corrections to four-dimensional CFT data and has potential applications to finite-coupling hydrodynamics.

Abstract

We examine five-dimensional $\mathcal N=2$ gauged supergravity including terms up to four derivatives. These additional terms correspond to the supersymmetric completion of $R^2$, and were originally obtained in hep-th/0611329 using conformal supergravity techniques. Here we integrate out the auxiliary fields and obtain the on-shell action for minimal supergravity with such corrections. We then construct $R$-charged AdS black holes to linear order in the four derivative terms and investigate the effect of these corrections on their thermodynamical properties. Finally, we relate the geometrical coefficients governing the four-derivative corrections to gauge theory data using holographic anomaly matching. This enables us to obtain a microscopic expression for the entropy of the solutions.