Near-horizon geometries and black hole thermodynamics in higher-derivative AdS5 supergravity

Abstract

Higher-derivative corrections in the AdS/CFT correspondence allow us to capture finer details of the dual CFT and to explore the holographic dictionary beyond the infinite N and strong coupling limits. Following an effective field theory approach, we investigate extremal AdS black hole solutions in five-dimensional supergravity with higher-derivative corrections. We provide a general analysis of near-horizon geometries of rotating extremal black holes and show how to obtain their corresponding charges and chemical potentials. We discuss the near-horizon solutions of the two-derivative theory, which we write using a novel parametrization that eases our computation of the higher-derivative corrections. The charges and thermodynamic properties of the black hole are computed while clarifying the ambiguities in their definitions. The charges and potentials turn out to satisfy a near-horizon version of the first law of thermodynamics whose interpretation we make clear. In the supersymmetric case, the results are shown to match the field theory prediction as well as previous results obtained from the on-shell action.

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

“…We have also derived the corrected supersymmetric and extremal black hole entropy as a function of the conserved charges by taking the Legendre transform of the action, see section 4.2. It would be interesting to perform a direct check of the expression for the corrected entropy, similarly to what was done in [6,83,103] for the minimal gauged supergravity solution. This check is currently out of reach as it requires knowledge of the corrected solution, or at least of the corrected near-horizon extremal solution.…”