Excited State Destri - De Vega Equation for Sine-Gordon and Restricted Sine-Gordon Models

TL;DR

This paper generalizes the Destri-De Vega equation to describe excited states in Sine-Gordon and Restricted Sine-Gordon models, linking their UV limits to conformal dimensions and minimal model perturbations.

Contribution

It introduces a generalized Destri-De Vega equation for excited states and connects these to conformal dimensions and minimal model perturbations.

Findings

Derived a generalized Destri-De Vega equation for excited states.

Matched UV limits to conformal dimensions of free boson.

Reconstructed scaling functions for off-critical primary states.

Abstract

We derive a generalization of the Destri - De Vega equation governing the scaling functions of some excited states in the Sine-Gordon theory. In particular configurations with an even number of holes and no strings are analyzed and their UV limits found to match some of the conformal dimensions of the corresponding compactified massless free boson. Quantum group reduction allows to interpret some of our results as scaling functions of excited states of Restricted Sine-Gordon theory, i.e. minimal models perturbed by phi_13 in their massive regime. In particular we are able to reconstruct the scaling functions of the off-critical deformations of all the scalar primary states on the diagonal of the Kac-table.