RSOS revisited

TL;DR

This paper examines the unitarity and spectral properties of imaginary affine Toda field theories with specific algebraic structures, revealing differences between models and proposing a new perspective on their spectra via projections of folded ATFTs.

Contribution

It provides a detailed analysis of the spectral reality in affine Toda models and corrects previous S-matrix conjectures, offering a novel approach to understanding RSOS spectra.

Findings

a_1(1) models have real spectra in finite volume

a_2(2) models generally have complex spectra

RSOS spectra can be derived from folded ATFTs via projections

Abstract

We investigate the issues of unitarity and reality of the spectrum for the imaginary coupled affine Toda field theories based on a_1(1) and a_2(2) and the perturbed minimal models that arise from their various RSOS restrictions. We show that while all theories based on a_1(1) have real spectra in finite volume, the spectra of a_2(2) models is in general complex, with some exceptions. We also correct the S matrices conjectured earlier for the phi(1,5) perturbations of minimal models and give evidence for a conjecture that the RSOS spectra can be obtained as suitable projections of the folded ATFTs in finite volume.