Three-loop universal structure constants in N=4 susy Yang-Mills theory

TL;DR

This paper conjectures the three-loop structure constants for twist two operators in N=4 super Yang-Mills theory, providing insights into the OPE structure constants through harmonic sums and asymptotic expansions.

Contribution

It introduces a conjecture for the three-loop normalization of twist two conformal partial waves in N=4 SYM, advancing understanding of structure constants at higher loops.

Findings

Conjectured three-loop structure constants expressed via harmonic sums.

Derived asymptotic expansions for complex three-loop integrals.

Enhanced methods for analyzing OPE data in supersymmetric theories.

Abstract

We present a conjecture for the normalisation of the twist two conformal partial waves in a double OPE limit of the four-point function of stress tensor multiplets in N = 4 super Yang-Mills theory up to three loops. This contains information about the structure constants in the OPE. Like the twist two anomalous dimensions our result is expressed as a linear combination of harmonic sums whose argument is the spin of the exchanged operators. To arrive at the result we derive asymptotic expansions for the twist two part of two unknown three-loop integrals using the method of expansion by regions, complemented by some intuition gained on the example of the ladder integrals up to three loops.