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

TL;DR

This paper develops an algorithm to construct matrix representations of the Virasoro algebra and chiral vertex operators for minimal conformal field theories, validated on several models, enhancing computational tools in conformal field theory.

Contribution

It introduces a level-by-level algorithm for building Virasoro and CVO representations using the L_1-basis, applicable to various minimal models and validated against known correlators.

Findings

Algorithm successfully constructs Virasoro modules for multiple models.

Results agree with known two-point functions for CVOs and energy-momentum tensor.

Provides a systematic basis relating to orthonormalized Virasoro states.

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.