Three-Point Functions in N=4 SYM Theory at One-Loop

Abstract

We analyze the one-loop correction to the three-point function coefficient of scalar primary operators in N=4 SYM theory. By applying constraints from the superconformal symmetry, we demonstrate that the type of Feynman diagrams that contribute depends on the choice of renormalization scheme. In the planar limit, explicit expressions for the correction are interpreted in terms of the hamiltonians of the associated integrable closed and open spin chains. This suggests that at least at one-loop, the planar conformal field theory is integrable with the anomalous dimensions and OPE coefficients both obtainable from integrable spin chain calculations. We also connect the planar results with similar structures found in closed string field theory.