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 ( α′ 3) corrections (or the leading corrections in powers of the eleven-dimensional Planck length, in the case of M-theory compactifications) 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. Surprisingly, for any of the considered dimension and topologies, the corrected thermodynamical quantities turn out to coincide with those calculated within a simplified approach, which uses only 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 α′ considerably smaller than that estimated previously by Gao and Li. Using the AdS/CFT correspondence, we determine the S 1 × 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 2 YM N ≈ 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. However, if the horizon is compactified to a torus T p or to a quotient of hyperbolic space, H p/Γ , the appearance of light winding modes around non-contractible cycles signal new phase transitions, which in the toroidal case have previously been discussed by Barbón et al. We comment on these phase transitions for SYM on H p/Γ and on T p , when the moduli of the torus are taken into account.