Spinons and parafermions in fermion cosets

TL;DR

This paper introduces gauge invariant fermion fields in fermionic coset models, elucidating their role in describing various conformal field theories, including minimal models, parafermions, and spinons, with potential applications in quantum Hall and spin-ladder systems.

Contribution

It provides explicit constructions of primary fields and operator product expansions in fermionic coset models, advancing the understanding of their structure and applications.

Findings

Realization of primaries and OPEs in minimal models

Explicit description of parafermion fields in Z_k CFTs

Representation of spinon fields in SU(N)_k WZW models

Abstract

We introduce a set of gauge invariant fermion fields in fermionic coset models and show that they play a very central role in the description of several Conformal Field Theories (CFT's). In particular we discuss the explicit realization of primaries and their OPE in unitary minimal models, parafermion fields in $Z_k$ CFT's and that of spinon fields in $SU(N)_k, k=1$ Wess-Zumino-Witten models (WZW) theories. The higher level case ($k>1$) will be briefly discussed. Possible applications to QHE systems and spin-ladder systems are addressed.