Parafermionic Representation of the Affine $sl(2/1)$ Algebra at Fractional Level

TL;DR

This paper presents a novel representation of the affine superalgebra $sl(2/1)$ at fractional level using parafermionic fields, scalar fields, and primary fields, expanding the understanding of its algebraic structure.

Contribution

It introduces a parafermionic representation of the affine $sl(2/1)$ algebra at fractional levels, linking it to free fields and parafermionic algebra structures.

Findings

Realization of fermionic currents via free scalar and parafermionic fields

Connection between $sl(2/1)$ at fractional level and parafermionic algebra $Z_{u-1}$

Explicit construction of algebraic representations at fractional levels

Abstract

The four fermionic currents of the affine superalgebra $sl(2/1)$ at fractional level $k=1/u-1$, u positive integer, are shown to be realised in terms of a free scalar field, an $sl(2)$ doublet field and a primary field of the parafermionic algebra $Z_{u-1}$.