Structure constants of planar Script N = 4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar N=4Yang-Mills at one loop with the motivation of determining features of thestring dual of weak coupling Yang-Mills. We derive a simple renormalizationgroup invariant formula characterizing the corrections to structure constantsof any primary operator in the planar limit. Applying this to the scalar SO(6)sector we find that the one loop corrections to structure constants of gaugeinvariant operators is determined by the one loop anomalous dimensionHamiltonian in this sector. We then evaluate the one loop corrections tostructure constants for scalars with arbitrary number of derivatives in a givenholomorphic direction. We find that the corrections can be characterized bysuitable derivatives on the four point tree function of a massless scalar withquartic coupling. We show that individual diagrams violating conformalinvariance can be combined together to restore it using a linear inhomogeneouspartial differential equation satisfied by this function.Comment: 52 pages, 12 figures, Typos fixed, reference adde