ADE spectra in conformal field theory

Bytsko, A. G. & Fring, A. (1999). ADE spectra in conformal field theory. Physics Letters B, 454(1-2), pp. 59-69. doi: 10.1016/S0370-2693(99)00300-7

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.