Computing Three-Point Functions for Short Operators

TL;DR

This work computes three-point structure constants for short operators in planar $\mathcal{N}=4$ SYM at leading order in $1/\sqrt{\lambda}$ by mapping to flat-space IIB string theory. Using twisted primary conditions to select suitable vertex operators, the authors derive explicit results for all combinations of chiral and level-one massive primaries, including the Konishi operator, and find numerous cancellations that yield remarkably simple expressions. The three-chiral-primaries case reproduces the known supergravity result, while mixed configurations reveal exponential suppression with the non-chiral states’ charges, suggesting a strong role for integrability in organizing these correlators. The findings provide strong-coupling targets for three-point functions and point toward deeper connections between AdS/CFT, flat-space string amplitudes, and integrable structures in ${\cal N}=4$ SYM.

Abstract

We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.