Classical correlation functions at strong coupling from hexagonalization

TL;DR

This paper investigates strong coupling correlation functions of half-BPS operators in planar $ ext{N}=4$ SYM using hexagon formalism, revealing their exponentiation and connection to TBA equations and wall-crossing techniques.

Contribution

It introduces a TBA-based framework for correlation functions at strong coupling, extending to polygonal and closed geometries via wall-crossing and $ ext{chi}$-systems.

Findings

Correlation functions exponentiate in the strong coupling regime.

TBA equations are structurally equivalent to BPS spectrum equations.

Generalization of minimal surface results to more complex geometries.

Abstract

We study correlation functions of half-BPS operators in planar $\mathcal{N}=4$ Super-Yang-Mills at strong coupling, in the classical limit where operator dimensions scale with the coupling. We focus on the two-dimensional kinematics corresponding in the dual description to strings propagating in $AdS_{3}\times S^{3}$. Using the hexagon formalism, we show that correlation functions exponentiate in this regime and are governed by the free energy of an associated set of Thermodynamic Bethe Ansatz (TBA) equations. These equations are structurally equivalent to the Gaiotto--Moore--Neitzke equations encoding BPS spectra in $\mathcal{N}=2$ supersymmetric field theories. Exploiting this correspondence, we apply wall-crossing techniques to extend the TBA framework and formulate a $\chi$-system applicable both to polygonal hexagon tilings and to closed geometries describing correlators of single-trace operators. In particular, for four-point functions, this construction generalizes the results of Caetano and Toledo for minimal surfaces in $AdS_{2}\times S^{1}$.