Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory

TL;DR

This paper introduces a non-perturbative integrability-based framework using hexagonal vertices to compute structure constants in planar N=4 SYM theory, simplifying the calculation of correlators across coupling regimes.

Contribution

It proposes a novel bootstrap approach for constructing three-point functions using elementary hexagonal vertices, advancing the integrability methods in N=4 SYM.

Findings

Predictions for three-point functions match weak and strong coupling data.

Hexagonal vertices provide a more elementary building block for correlator computations.

Framework offers a non-perturbative method for structure constants in large N limit.

Abstract

We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and possibly higher-point correlators. These newborn hexagons are more elementary and easier to deal with than the three-point functions. Moreover, they can be entirely constructed using integrability, by means of a suitable bootstrap program. In this letter, we present our main results and conjectures for these vertices, and match their predictions for the three-point functions with both weak and strong coupling data available in the literature.