Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory

TL;DR

This paper proposes an integrability-based conjecture for three-point functions in planar T super-Yang-Mills theory, extending the hexagon approach to finite coupling and testing it against gauge and string theory results.

Contribution

It introduces a new conjecture for structure constants involving any operator length, combining hexagon formalism with TBA/QSC data, and validates it at multiple coupling regimes.

Findings

Agreement with gauge theory at 5 loops for shortest operators

Consistency with string theory in the classical limit

Extension of the hexagon formalism to finite coupling and arbitrary operator length

Abstract

We present an integrability-based conjecture for the three-point functions of single-trace operators in planar $\mathcal{N}=4$ super-Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA/QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.