M-theory and stringy corrections to anti-de Sitter black holes and conformal field theories

We consider black holes in anti-de Sitter space AdS(p+2) (p = 2, 3, 5), whi ch have hyperbolic, flat or spherical event horizons. The O(alpha'(3)) corr ections (or the leading corrections in powers of the eleven-dimensional Pla nck length, in the case of M-theory compactifications) to the black hole me trics are computed for the various topologies and dimensions. We investigat e the consequences of the stringy or M-theory corrections for the black hol e thermodynamics. In particular, we show the emergence of a stable branch o f small spherical black holes. Surprisingly, for any of the considered dime nsions and topologies, the corrected thermodynamical quantities turn out to coincide with those calculated within a simplified approach, which uses on ly the unperturbed metric. 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 smalle r than that estimated previously by Gao and Li. Using the AdS/CFT correspon dence, 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 Hawk ing-Page transition disappears (the correspondence point of Horowitz-Polchi nski), occurs at g(YM)(2)N approximate to 20.5. The d = 4 and d = 7 black h ole phase diagrams are also determined, and connection is made with the cor responding boundary CFTs. Finally, for flat and hyperbolic horizons, we sho w that the leading stringy or M-theory corrections do not give rise to any phase transition. However, if the horizon is compactified to a torus TP or to a quotient of hyperbolic space, H-p/Gamma, the appearance of light windi ng modes around non-contractible cycles signal new phase transitions, which in the toroidal case have previously been discussed by Barbon et al. We co mment on these phase transitions for SYM on H-p/Gamma and on TP, when the m oduli of the torus are taken into account. (C) 1999 Published by Elsevier S cience B.V. All rights reserved.