Gravity duals of fractional branes and logarithmic RG flow

We study fractional branes in N = 2 orbifold and N = 1 conifold theories. Placing a large number N of regular D3-branes at the singularity produces the dual AdS(5) x X-5 geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, X-5 = S-5/Gamma and fractional D3-branes excite complex scalars from the: twisted sector which are localized on the fixed circle of X-5. The resulting solutions are given by holomorphic functions and the field-theoretic beta-function is simply reproduced. For N regular and M fractional D3-branes at the conifold singularity we find a non-conformal N = 1 supersymmetric SU(N + M) x SU(N) gauge theory. The dual Type IB background is AdS(5) x T-1.1 with NS-NS and R-R 2-form fields turned on. This dual description reproduces the logarithmic flow of couplings found in the field theory. (C) 2000 Elsevier Science B.V. All rights reserved.