Abstract :
We discuss string theory image corrections to charged near-extremal black 3-branes/black holes in type IIB supergravity. We find that supersymmetric global image geometry is not corrected to leading order in image, while charged or non-extremal black 3-branes/black hole geometries receive image corrections. Following gauge theory-string theory correspondence the thermodynamics of these geometries is mapped to the thermodynamics of large-image image supersymmetric Yang–Mills theory at finite (large) ʹt Hooft coupling with the image-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 image corrected thermodynamics of black holes in image and the thermodynamics of charged black 3-branes with identical chemical potentials for image charges and large (compare to chemical potential) temperature. We compute image corrections to Hawking–Page phase transition. We find that for nonzero chemical potential thermodynamics of near-extremal black 3-brane solution receives image correction to leading order in image.
