S-Matrices of $\phi_{1,2}$ perturbed unitary minimal models: IRF-Formulation and Bootstrap-Program

TL;DR

This paper explores the algebraic structure of $_{1,2}$ perturbed minimal models, connecting them to graph-state models and the Birman-Wenzl-Murakami algebra, to clarify physical properties and compute the S-matrix and spectrum.

Contribution

It introduces a novel algebraic framework relating perturbed minimal models to graph-state models and uses it to reformulate bootstrap equations and compute spectra.

Findings

Calculated S-matrix elements for higher kinks

Determined breather spectrum of $_{1,2}$ perturbations

Clarified physical properties of perturbed models

Abstract

We analyze the algebraic structure of $\phi_{1,2}$ perturbed minimal models relating them to graph-state models with an underlying Birman-Wenzl-Murakami algebra. Using this approach one can clarify some physical properties and reformulate the bootstrap equations. These are used to calculate the $S$-matrix elements of higher kinks, and to determine the breather spectrum of the $\phi_{1,2}$ perturbations of the unitary minimal models $\M_{r,r+1}$.