Structure Constants from Q-Systems and Separation of Variables

TL;DR

The paper presents a new method to compute structure constants in N=4 SYM using Q-functions and separation of variables, connecting to existing formalisms and applicable to integrable models.

Contribution

It introduces a determinant-based approach to structure constants from Q-functions, linking to the Hexagon formalism and extending to twisted operators.

Findings

Structure constants expressed as determinants of matrices with Q-function integrals.

Matching with Hexagon formalism in the untwisting limit.

Framework applicable at leading order and extendable to loop corrections.

Abstract

We introduce a novel method to compute structure constants from Q-functions in the scalar sector of planar N=4 super Yang-Mills (SYM) and related theories. The method derives from operatorial as well as functional separation of variables, and the structure constants are expressed as determinants of matrices whose entries are integrals over products of Q-functions. In this framework, each operator is twisted by an external angle, mirroring the cusped Maldacena-Wilson loop. The structure constants of local single-trace operators in N=4 SYM are recovered in the untwisting limit, where we obtain a one-to-one correspondence between our key building blocks and those of the Hexagon formalism. Retaining appropriate twists, our structure constants also perfectly match those of the orbifold points of N=4 SYM. Our results thus far are valid at leading order in the weak-coupling expansion, but their formulation in terms of Q-functions provides a natural starting point for including loop corrections. Many of the methods we develop in this work apply more generally to the computation of correlation functions in integrable models.