Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields

Abstract

We consider sl(2) minimal conformal field theories and the dual parafermion models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS) models and its Virasoro modules expressed in terms of paths, we propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). We implement our scheme for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories on a cylinder and confirm that it is consistent with the known two-point functions for the CVOs and energy-momentum tensor. Our algorithm employs a distinguished basis which we call the L_1-basis. We relate the states of this canonical basis level-by-level to orthonormalized Virasoro states.

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

Cited by in corpus (13)

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• Continuum limit and symmetries of the periodic gl(1|1) spin chain
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• Excited TBA Equations II: Massless Flow from Tricritical to Critical Ising Model
• Finite-Volume Spectra of the Lee-Yang Model
• On the Integrable Structure of the Ising Model
• Paths and partitions: combinatorial descriptions of the parafermionic states
• Physical Combinatorics and Quasiparticles
• Lattice Integrals of Motion of the Ising Model on the Cylinder
• Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models
• Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• Local height probabilities in a composite Andrews-Baxter-Forrester model