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

We discuss string theory α corrections to charged near-extremal black 3-branes/black holes in type IIB supergravity. We find that supersymmetric global AdS5 × S 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-nc 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 AdS5×S 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 lnT correction to leading order in α.