Crystalline Spinon Basis for RSOS Models

TL;DR

This paper develops a crystalline spinon basis for RSOS models related to a9sl_2, providing fermionic character formulas and linking path descriptions of parafermion characters to spinon descriptions.

Contribution

It introduces a new crystalline spinon basis for RSOS models and connects it to fermionic character formulas and path descriptions of parafermion characters.

Findings

Provides fermionic character formulas for coset branching coefficients

Establishes a path description of parafermion characters as a limit of spinon descriptions

Enhances understanding of the structure of RSOS models and related characters

Abstract

The crystalline spinon basis for the RSOS models associated with $\widehat{sl_2}$ is studied. This basis gives fermionic type character formulas for the branching coefficients of the coset $(\widehat{sl_2})_l \times (\widehat{sl_2})_N/(\widehat{sl_2})_{l+N}$. In addition the path description of the parafermion characters is found as a limit of the spinon description of the string functions.