From path representations to global morphisms for a class of minimal models

TL;DR

This paper constructs global observable algebras and superselection sectors for Virasoro minimal models using path representations and quantum symmetries, providing a new framework for understanding their structure.

Contribution

It introduces a novel approach to minimal models by passing from highest weight modules to path representations and employing quantum symmetries to build global morphisms.

Findings

Path algebras serve as bounded observable algebras

Quantum symmetries act on path spaces

Global morphisms implement superselection sectors

Abstract

We construct global observable algebras and global DHR morphisms for the Virasoro minimal models with central charge c(2,q), q odd. To this end, we pass {}from the irreducible highest weight modules to path representations, which involve fusion graphs of the c(2,q) models. The paths have an interpretation in terms of quasi-particles which capture some structure of non-conformal perturbations of the c(2,q) models. The path algebras associated to the path spaces serve as algebras of bounded observables. Global morphisms which implement the superselection sectors are constructed using quantum symmetries: We argue that there is a canonical semi-simple quantum symmetry algebra for each quasi-rational CFT, in particular for the c(2,q) models. These symmetry algebras act naturally on the path spaces, which allows to define a global field algebra and covariant multiplets therein.