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 N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super-Yang-Mills theory. The Lagrangian insertion method, together with symmetries of the theory fix the integrand up to a few constants. Under the additional assumption of planarity, all these constants can be determined by lower loop data. The obtained result can be regarded as the planar diagram contribution to the full four-point function and is 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.