Free boson representation of DY_{\hbar}(gl_N)_k

TL;DR

This paper constructs a free boson realization of the Yangian double DY_ar(gl_N) and DY_
bar(sl_N) at arbitrary level k, connecting to Wakimoto realization in the classical limit and developing vertex operators and screening currents.

Contribution

It provides a novel free boson representation of the Yangian double for arbitrary level, extending Wakimoto realization and constructing associated vertex operators and screening currents.

Findings

Realization of DY_
bar(gl_N) and DY_
bar(sl_N) using free boson fields.

In the classical limit, the realization reduces to Wakimoto realization.

Constructed vertex operators and screening currents compatible with the algebra.

Abstract

We construct a realization of the Yangian double DY_\hbar(gl_N) and DY_\hbar(sl_N) of an arbitrary level k in terms of free boson fields with a continuous parameter. In the \hbar \to 0 limit this realization becomes the Wakimoto realization of kac-Moody algebra gl_N and sl_N, respectively. The vertex operators and the screening currents are also constructed with the same spirits; the screening currents commute with DY_\hbar(sl_N) modulo total difference.