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

TL;DR

This paper investigates alpha' string theory corrections to near-extremal black holes in type IIB supergravity, revealing that certain geometries are uncorrected while others receive specific thermodynamic modifications, including phase transition shifts.

Contribution

It provides explicit alpha' corrected thermodynamic expressions for charged near-extremal black holes in AdS_5 x S^5, including phase transition analysis, extending holographic thermodynamics at finite chemical potential.

Findings

Supersymmetric AdS_5 x S^5 geometry remains uncorrected at leading order.

Charged black 3-branes receive alpha' corrections affecting thermodynamics.

Alpha' corrections introduce a ln T term in the thermodynamics at finite chemical potential.

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'.