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

Abstract

We discuss string theory α ′ corrections to charged near-extremal black 3-branes/black holes in type IIB supergravity. We find that supersymmetric global AdS 5 × S 5 geometry is not corrected to leading order in α ′ , while charged or non-extremal black 3-branes/black hole geometries receive α ′ 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 α ′ corrected thermodynamics of black holes in AdS 5 × 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 α ′ 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 α ′ .