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

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

1996-12-17

arxiv.org/abs/hep-th/9612178v1

Commun.Math.Phys. 201 (1999) 365-409

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, Plain TeX, 2 figures

Scientific paper

10.1007/s002200050559

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.

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