Graded parafermions: standard and quasi-particle bases

TL;DR

This paper introduces two different bases for modules of graded parafermionic conformal field theory, revealing structural properties like reducibility and a hidden  exclusion principle.

Contribution

It presents a new quasi-particle basis based on a modified exclusion principle and uncovers a hidden  symmetry in the structure of the modules.

Findings

Explicit form of singular vectors in the first basis

Identification of reducible representations

Discovery of a hidden  exclusion principle

Abstract

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset $\osp(1,2)_k/\uh(1)$. The first one is formulated in terms of the two fundamental (i.e., lowest dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasi-particle basis, determined in terms of a modified version of the $\ZZ_{2k}$ exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural $\Z_3$ exclusion principle.