String corrections to the holographic RG flow of supersymmetric SU(N + M) × SU(N) gauge theory

We study leading string corrections to the type IIB supergravity solution dual to the N = 1 supersymmetric SU(N + M) × SU(N) gauge theory coupled to bifundamental chiral superfields A_i, B_j, i, j = 1, 2. This solution was found in hep-th/0007191, and its asymptotic form describing logarithmic RG flow was constructed in hep-th/0002159. The leading tree-level string correction to the type IIB string effective action is represented by the invariant of the form α′³(R⁴ + ⋯). Since the background contains 3-form field strengths, we need to know parts of this invariant that depend on them. By analyzing the 5-point superstring scattering amplitudes we show that only a few specific R³(H ₃)² and R³(F₃)² terms are present in the effective action. Their contribution to the holographic RG flow turns out to be of the same order as of the R⁴ terms. Using this fact we show that it is possible to have agreement between the α′- corrected radial dependence of the supergravity fields and the RG flow dictated by the NSVZ beta functions in field theory. The agreement with field theory requires that the anomalous dimension of the operators Tr(A_iB _j) is corrected by a term of order (M/N)⁴λ ^-1/2 from its value -1/2 found for M = 0 (λ is the appropriate't Hooft coupling which is assumed to be strong).