Classical limit of diagonal form factors and HHL correlators

TL;DR

This paper develops a method to compute the classical limit of diagonal form factors by integrating over classical solutions' moduli space, connecting it to finite volume effects and classical Bethe-Yang equations, with applications to sine-Gordon models.

Contribution

It introduces a new integral expression for the classical limit of diagonal form factors, including regularization in infinite volume and finite volume formulations, and relates these to classical Bethe-Yang equations.

Findings

Derived a regularized integral expression for classical diagonal form factors.

Established a classical analogue of Bethe-Yang equations for finite volume.

Applied the framework to heavy-heavy-light three-point functions in sine-Gordon theory.

Abstract

We propose an expression for the classical limit of diagonal form factors in which we integrate the corresponding observable over the moduli space of classical solutions. In infinite volume the integral has to be regularized by proper subtractions and we present the one, which corresponds to the classical limit of the connected diagonal form factors. In finite volume the integral is finite and can be expressed in terms of the classical infinite volume diagonal form factors and subvolumes of the moduli space. We analyze carefully the periodicity properties of the finite volume moduli space and found a classical analogue of the Bethe-Yang equations. By applying the results to the heavy-heavy-light three point functions we can express their strong coupling limit in terms of the classical limit of the sine-Gordon diagonal form factors.