Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules

Details Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules

2002-11-20

arxiv.org/abs/hep-th/0211185v1

Nucl.Phys. B663 (2003) 409-442

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

We consider sl(2) minimal conformal field theories on a cylinder from a lattice perspective. To each allowed one-dimensional configuration path of the A_L Restricted Solid-on-Solid (RSOS) models we associate a physical state |h> and a monomial in a finite fermionic algebra. The orthonormal states produced by the action of these monomials on the primary states generate finite Virasoro modules with dimensions given by the finitized Virasoro characters $\chi^{(N)}_h(q)$. These finitized characters are the generating functions for the double row transfer matrix spectra of the critical RSOS models. We argue that a general energy-preserving bijection exists between the one-dimensional configuration paths and the eigenstates of these transfer matrices and exhibit this bijection for the critical and tricritical Ising models in the vacuum sector. Our results extend to Z_{L-1} parafermion models by duality.

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