Classification of Conformal Field Theories Based on Coulomb gases. Application to Loop Models

TL;DR

This paper introduces a new classification method for conformal field theories using Coulomb gases, extending beyond classical Lie algebra frameworks, and applies it to loop models to clarify their symmetries.

Contribution

It develops a generalized classification approach for conformal field theories based on Coulomb gases and demonstrates its application to specific loop models.

Findings

Classification conditions for degenerate representations

Extended symmetry relations in Coulomb gas models

Application to two-flavoured loop model

Abstract

We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.