Spectrum of the reflection operators in different integrable structures

TL;DR

This paper provides a comprehensive analysis of the spectrum of reflection operators in various integrable conformal field theories, revealing their structure and relations, with implications for solvable lattice models and statistical mechanics.

Contribution

It presents the full spectrum of reflection operators for multiple integrable structures and establishes a relation between their S-matrices in Liouville and cigar CFTs.

Findings

Spectrum of reflection operators determined for several integrable models

Relation established between cigar and Liouville CFT S-matrices

Results applicable to Bethe state scaling and generalized Gibbs ensembles

Abstract

The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are built from the (chiral) reflection S-matrices for the Liouville and cigar CFTs. Here we give the full spectrum of the reflection operators associated with these integrable structures. We also obtained a relation between the reflection S-matrices of the cigar and Liouville CFTs. The results of this work are applicable for the description of the scaling behaviour of the Bethe states in exactly solvable lattice systems and may be of interest to the study of the Generalized Gibbs Ensemble associated with the above mentioned integrable structures.