Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability

TL;DR

This paper explores how integrability and dispersive sum rules can be combined to determine and bound correlation functions in planar $ ext{N}=4$ super Yang-Mills theory, including nonperturbative regimes.

Contribution

It introduces a method to bootstrap four-point correlators using integrability data and sum rules, providing new bounds on OPE coefficients beyond perturbation theory.

Findings

Constructed sum rule combinations for one-loop correlators.

Numerically bounded planar OPE coefficients nonperturbatively.

Observed cusps at physical operator locations in the bounds.

Abstract

How much spectral information is needed to determine the correlation functions of a conformal theory? We study this question in the context of planar supersymmetric Yang-Mills theory, where integrability techniques accurately determine the single-trace spectrum at finite 't Hooft coupling. Corresponding OPE coefficients are constrained by dispersive sum rules, which implement crossing symmetry. Focusing on correlators of four stress-tensor multiplets, we construct combinations of sum rules which determine one-loop correlators, and we study a numerical bootstrap problem that nonperturbatively bounds planar OPE coefficients. We observe interesting cusps at the location of physical operators, and we obtain a nontrivial upper bound on the OPE coefficient of the Konishi operator outside the perturbative regime.