Free Field Realizations of 2D Current Algebras, Screening Currents and Primary Fields

TL;DR

This paper advances the understanding of 2D current algebras by providing new free field realizations, explicit primary field constructions, and detailed properties of screening currents, facilitating the computation of correlators in complex representations.

Contribution

It introduces simplified universal expressions for currents, proves properties of screening currents of the second kind, and constructs explicit primary fields with non-integer weights.

Findings

Derived compact expressions for all currents.

Proved properties of screening currents of the second kind.

Constructed explicit primary fields with non-integer weights.

Abstract

In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results. (i) Based on quantizing differential operator realizations of the corresponding Lie algebras we provide general universal very simple expressions for all currents, more compact than has been established so far. (ii) We supplement the treatment of screening currents of the first kind, known in the literature, by providing a direct proof of the properties for screening currents of the second kind. Finally (iii) we work out explicit free field realizations of primary fields with general non-integer weights. We use a formalism where the (generally infinite) multiplet is replaced by a generating function primary operator. These results taken together allow setting up integral representations for correlators of primary fields corresponding to non-integrable degenerate (in particular admissible) representations.