M-Theory and Stringy Corrections to Anti-de Sitter Black Holes and Conformal Field Theories
Marco M. Caldarelli, Dietmar Klemm
TL;DR
The paper analyzes how stringy and M-theory corrections modify AdS black holes with spherical, flat, or hyperbolic horizons and maps these bulk effects to phase structures in dual CFTs. By incorporating Weyl^4-type corrections and performing a perturbative analysis, it derives corrected free energies, entropies, and metrics for d=4,5,7 cases, revealing a stable small BH branch and a lowered Hawking-Page transition, with explicit phase diagrams for SYM on S^1×S^3 and related theories. A key result is the Horowitz–Polchinski correspondence point at $g_{YM}^2N \approx 20.5$, where the first-order transition degenerates, and the finding that flat or simply connected hyperbolic horizons do not develop phase transitions under leading corrections (except for finite-size winding effects). The work strengthens the AdS/CFT dictionary by linking higher-curvature bulk corrections to finite-temperature boundary dynamics and provides a framework for including winding-mode effects on compactifications.
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 $O(α'^3)$ 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 $α'$ 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, $H^p/Γ$, we comment on the effects of light winding modes.