Strong coupling limit of N=2 SCFT free energy and higher derivative AdS/CFT correspondence

We study the role of higher derivative terms (Riemann curvature squared one s) in thermodynamics of SCFTs via AdS/CFT correspondence. Using HB string e ffective action (d5 AdS gravity) with such HD terms deduced from heterotic string via duality we calculate strong coupling limit of N = 2 SCFT free en ergy with the account of next to leading term in large N expansion. It is c ompared with perturbative result following from boundary QFT. Considering m odification of such action where HD terms form Weyl squared tensor we found (strong coupling limit) free energy in such theory. It is interesting that leading and next to leading term of large N expanded free energy may diffe r only by factor 3/4 if compare with perturbative result. Considering HD gr avity as bosonic sector of some (compactified) HD supergravity we suggest n ew version of AdS/CFT conjecture and successfully test it on the level of f ree energies for N = 2,4 SCFTs. (C) 1999 Published by Elsevier Science B.V. All rights reserved.