M-Theory and Stringy Corrections to Anti-de Sitter Black Holes and Conformal Field Theories

TL;DR

This paper computes stringy and M-theory corrections to AdS black hole metrics across various topologies and dimensions, analyzing their effects on thermodynamics, phase transitions, and dual conformal field theories, revealing new stable phases and critical points.

Contribution

It provides the first detailed calculation of $O(\alpha'^3)$ corrections for AdS black holes with different topologies and explores their implications for black hole thermodynamics and AdS/CFT phase diagrams.

Findings

Emergence of a stable small black hole branch.

Corrected Hawking-Page transition temperature and its disappearance.

Critical 't Hooft coupling for phase transition in N=4 SYM at approximately 20.5.

Abstract

We consider black holes in anti-de Sitter space AdS_{p+2} (p = 2,3,5), which have hyperbolic, flat or spherical event horizons. The $O(\alpha'^3)$ corrections (or the leading corrections in powers of the eleven-dimensional Planck length) to the black hole metrics are computed for the various topologies and dimensions. We investigate the consequences of the stringy or M-theory corrections for the black hole thermodynamics. In particular, we show the emergence of a stable branch of small spherical black holes. We obtain the corrected Hawking-Page transition temperature for black holes with spherical horizons, and show that for p=3 this phase transition disappears at a value of $\alpha'$ considerably smaller than that estimated previously by Gao and Li. Using the AdS/CFT correspondence, we determine the $S^1 x S^3$ N=4 SYM phase diagram for sufficiently large `t Hooft coupling, and show that the critical point at which the Hawking-Page transition disappears (the correspondence point of Horowitz-Polchinski), occurs at $g_{YM}^2N \approx 20.5$. The d=4 and d=7 black hole phase diagrams are also determined, and connection is made with the corresponding boundary CFTs. Finally, for flat and hyperbolic horizons, we show that the leading stringy or M-theory corrections do not give rise to any phase transition. For horizons compactified to a torus $T^p$ or to a quotient of hyperbolic space, $H^p/\Gamma$, we comment on the effects of light winding modes.