Mm. Caldarelli et D. Klemm, M-theory and stringy corrections to anti-de Sitter black holes and conformal field theories, NUCL PHYS B, 555(1-2), 1999, pp. 157-182
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.