A Note on ADE-Spectra in Conformal Field Theory

TL;DR

This paper explores the relationship between ADE-series Virasoro characters in conformal field theory and Lie algebraic quasi-particle spectra, revealing connections to Toda field theory and $W_n$-generators.

Contribution

It uncovers the ADE classification in Virasoro characters and links them to Lie algebraic spectra and Toda field theory, providing new insights into their structure.

Findings

Virasoro characters relate to ADE series and Toda field theory.

Interrelations between parafermionic models, compactified bosons, and minimal models.

Potential construction of spectra using $W_n$-generators.

Abstract

We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasi-particle spectra of a Lie algebraic nature which resembles the features of Toda field theory. These spectra possibly admit a construction in terms of the $W_n$-generators. In the course of our analysis we establish interrelations between the factorized characters related to the parafermionic models, the compactified boson and the minimal models.