On a Bosonic-Parafermionic Realization of $U_q(\widehat{sl(2)})$

TL;DR

This paper constructs a realization of the quantum affine algebra $U_q(\\widehat{sl(2)})$ using deformed bosonic and parafermionic fields, revealing complex operator product expansions and connecting to known models at specific levels.

Contribution

It introduces a novel realization of $U_q(\widehat{sl(2)})$ at arbitrary level with deformed fields, extending previous models and analyzing their operator product structures.

Findings

Operator product expansions involve infinite poles and zeros.

Condensation forms a branch cut in the classical limit.

Realization matches known models at levels 1 and 2.

Abstract

We realize the $U_q(\widehat{sl(2)})$ current algebra at arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limit $q\rightarrow 1$. Our realization coincides with those of Frenkel-Jing and Bernard when the level $k$ takes the values 1 and 2 respectively.