A Free Field Representation of the Screening Currents of $U_q(\widehat{sl(3)})

TL;DR

This paper constructs explicit screening currents for the quantum affine algebra U_q(sl(3)), expressing them via deformed bosonic fields, which advances understanding of quantum current algebra representations.

Contribution

It provides a free field realization of the screening currents for U_q(sl(3)), including a novel infinite sum expression for one of the currents.

Findings

Five independent screening currents constructed

Screening currents expressed as exponentials of deformed bosonic fields

Structure likely similar for general quantum affine algebras

Abstract

We construct five independent screening currents associated with the $U_q(\widehat{sl(3)})$ quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the quantum analogue of the Wakimoto realization of the current algebra. Four of the screening currents are `simple', in that each one is given as a single exponential field. The fifth is expressed as an infinite sum of exponential fields. For reasons we discuss, we expect that the structure of the screening currents for a general quantum affine algebra will be similar to the $U_q(\widehat{sl(3)})$ case.