Higher derivative corrections to near-extremal black holes in type IIB supergravity

TL;DR

This work analyzes leading α' corrections to the thermodynamics of charged near-extremal black holes in type IIB string theory on AdS$_5\times S^5$. By embedding the STU models into ten-dimensional IIB supergravity and employing holographic renormalization, Buchel derives analytic α'–corrected expressions for the Gibbs free energy, ADM mass, entropy, and other thermodynamic potentials for neutral and equal-charge black holes/branes, including the Hawking-Page transition. A key finding is that global AdS$_5\times S^5$ is not corrected at leading order, while nonzero chemical potential introduces a logarithmic temperature dependence in the charged, κ=0 case, manifested as a $\ln T$ term in the Gibbs free energy. The results also reveal an emergent energy scale $\epsilon$ and suggest a renormalization-group–like running of the effective coupling at finite temperature and chemical potential, offering insight into finite-coupling dynamics of ${\cal N}=4$ SYM via holography.

Abstract

We discuss string theory alpha' corrections to charged near-extremal black 3-branes/black holes in type IIB supergravity. We find that supersymmetric global AdS_5 x S^5 geometry is not corrected to leading order in alpha', while charged or non-extremal black 3-branes/black hole geometries receive alpha' corrections. Following gauge theory-string theory correspondence the thermodynamics of these geometries is mapped to the thermodynamics of large-n_c N=4 supersymmetric Yang-Mills theory at finite (large) 't Hooft coupling with the U(1)_R-charge chemical potential. We use holographic renormalization to compute the Gibbs free energy and the ADM mass of the near-extremal solutions. The remaining thermodynamic potentials are evaluated enforcing the first law of thermodynamics. We present analytic expressions for the alpha' corrected thermodynamics of black holes in AdS_5 x S^5 and the thermodynamics of charged black 3-branes with identical chemical potentials for [U(1)_R]^3 charges and large (compare to chemical potential) temperature. We compute alpha' corrections to Hawking-Page phase transition. We find that for nonzero chemical potential thermodynamics of near-extremal black 3-brane solution receives ln T correction to leading order in alpha'.