Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM

TL;DR

This paper develops a systematic method linking correlation functions on the Maldacena-Wilson line in N=4 SYM to integrability data, enabling new constraints on multi-point functions via the Quantum Spectral Curve.

Contribution

It introduces a novel approach to connect Wilson line correlators with integrability data, facilitating the derivation of numerous constraints on correlation functions in N=4 SYM.

Findings

Derived relations connecting Wilson line correlators with integrability data.

Established a framework for constraints on multi-point correlation functions.

Potential to improve non-perturbative bounds using these constraints.

Abstract

We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.