Higher derivative corrections to near-extremal black holes in type IIB   supergravity
  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'. 
Alex Buchel