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

Abstract

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 ${\chi }_h^{(N)}(q)$. 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.

References in corpus (2)

• Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model
• Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder

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• Physical Combinatorics and Quasiparticles
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