Restricted Quantum Affine Symmetry of Perturbed Minimal Models

TL;DR

This paper explores how restricting quantum affine symmetry in perturbed minimal models helps derive S-matrices, identify fields creating kink spectra, and relate to Fock space cohomology, revealing fractional supersymmetry structures.

Contribution

It introduces a method to derive S-matrices and analyze the structure of perturbed minimal models using restricted quantum affine symmetry, including new insights into degenerate vacua and fractional supersymmetry.

Findings

Derived S-matrices for $ ext{Phi}^{(1,3)}$ perturbations.

Identified fields creating the massive kink spectrum.

Connected restriction procedures to Fock space cohomology and fractional supersymmetry.

Abstract

We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the $\Phi^{(1,3)}$ perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. We investigate the ultraviolet limit of the restricted sine-Gordon model, and explain the relation between the restriction and the Fock space cohomology of minimal models. We also comment on the structure of degenerate vacuum states. Deformed Serre relations are proven for arbitrary affine Toda theories, and it is shown in certain cases how relations of the Serre type become fractional spin supersymmetry relations upon restriction.