Exact mass-coupling relation for the homogeneous sine-Gordon model

TL;DR

This paper derives an exact relation between masses and couplings in the homogeneous sine-Gordon model, using conformal field theory and bootstrap methods, expressed through hypergeometric functions.

Contribution

It provides the first exact mass-coupling relation for the two-scale homogeneous sine-Gordon model, connecting short-distance CFT and large-distance integrability approaches.

Findings

Derived a differential equation for the mass-coupling relation.

Expressed the relation explicitly using hypergeometric functions.

Established a link between conformal perturbation theory and bootstrap methods.

Abstract

We derive the exact mass-coupling relation of the simplest multi-scale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents which satisfy a generalization of the $\Theta$ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.