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

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.

50 pages, Plain TeX, 2 figures

References in corpus (10)

• Quasi-particles models for the representations of Lie algebras and geometry of flag manifold
• Fusion of twisted representations
• Lift of dilogarithm to partition identities
• Subfactors and coset models
• Path Spaces and W-Fusion in Minimal Models
• Virasoro Representations on Fusion Graphs
• Reminiscences about Many Pitfalls and Some Successes of QFT Within the Last Three Decades
• Pathspace Decompositions for the Virasoro Algebra and its Verma Modules
• Generalization of the Knizhnik-Zamolodchikov-Equations
• Towards a classification of rational Hopf algebras