Anti-de-Sitter black hole thermodynamics in higher derivative gravity and new confining-deconfining phases in dual CFT

The thermodynamics of d5 AdS BHs with positive, negative or zero curvature spatial section in higher derivative (HD) gravity is described. HID contrib ution to free energy may change its sign which leads to more complicated re gime for Hawking-Page phase transitions. Some variant of d5 HD gravity is d ual to N = 2 Sp(N) SCFT up to the next-to-leading order in large N. Then, a ccording to Witten interpretation the stable AdS BH phase corresponds to de confinement while global AdS phase corresponds to confinement. Unlike to Ei nstein gravity in ED theory the critical N appears. It may influence the ph ase transition structure. In particular, what was confining phase above the critical value becomes the deconfining phase below it and vice-versa. (C) 2001 Published by Elsevier Science B.V.