A New Family of Diagonal Ade-Related Scattering Theories

TL;DR

This paper introduces a new family of diagonal scattering theories related to non-unitary minimal models, extending the $E_8$ scattering theory, and explores their thermodynamic properties and generalizations to coset models.

Contribution

It proposes a novel family of diagonal ADE-related scattering theories for non-unitary models, generalizing the $E_8$ theory and including magnonic TBA for coset models.

Findings

Relation to $E_8$ minimal scattering theory

Development of non-unitary diagonal ADE-related theories

Extension to non-diagonal S-matrices for coset models

Abstract

We propose the factorizable S-matrices of the massive excitations of the non-unitary minimal model $M_{2,11}$ perturbed by the operator $\Phi_{1,4}$. The massive excitations and the whole set of two particle S-matrices of the theory is simply related to the $E_8$ unitary minimal scattering theory. The counting argument and the Thermodynamic Bethe Ansatz (TBA) are applied to this scattering theory in order to support this interpretation. Generalizing this result, we describe a new family of NON UNITARY and DIAGONAL $ADE$-related scattering theories. A further generalization suggests the magnonic TBA for a large class of non-unitary $\G\otimes\G/\G$ coset models ($\G=A_{odd},D_n,E_{6,7,8}$) perturbed by $\Phi_{id,id,adj}$, described by non-diagonal S-matrices.