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

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 $O({\alpha }^{\prime 3})$ 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 ${\alpha }^{\prime }$ 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 $g_{YM}^{2}N\approx 20.5$. 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.

29 pages, revtex, 6 figures using epsfig, typos corrected, 1 reference added, final version to appear in Nucl. Phys. B

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