Three-point functions of twist-two operators in $ \mathcal{N}=4 $ SYM at one loop

Abstract

We calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory to one-loop order. In order to carry out the calculations we project the indices of the spin j operator to the light-cone and evaluate the correlator in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The results of our direct calculation are in agreement with the structure constants obtained by F.A. Dolan and H. Osborn from the operator product expansion of four-point functions of half-BPS operators.