Giant Correlators at Quantum Level

Abstract

We compute four-point functions with two maximal giant gravitons and two chiral primary operators at three-loop order in planar $\mathcal{N}=4$ Super-Yang-Mills theory. The Lagrangian insertion method, together with symmetries of the theory fix the integrand up to a few constants, which can be determined by lower loop data. The final result can be written in terms of the known three-loop conformal integrals. From the four-point function, we extract the OPE coefficients of two giant gravitons and one non-BPS twist-2 operator with arbitrary spin at three-loops, given in terms of harmonic sums. We observe an intriguingly simple relation between the giant graviton OPE coefficients and the OPE coefficients of three single-trace operators.