Gravity duals of fractional branes and logarithmic RG flow

We study fractional branes in script N = 2 orbifold and script N = 1 conifold theories. Placing a large number N of regular D3-branes at the singularity produces the dual AdS₅ × X⁵ geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, X⁵ = S⁵/Γ and fractional D3-branes excite complex scalars from the twisted sector which are localized on the fixed circle of X⁵. 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 script N = 1 supersymmetric SU(N + M) × SU(N) gauge theory. The dual Type IB background is AdS₅ × 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.