Free field realizations of 2D current algebras, screening currents and primary fields

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.

algebras

“…We use the notation C n λ 1 (z) for this space, which is the evaluation representation of sℓ(n) (with the subscript λ 1 intended to distinguish it from other copies of C n ). In the Wakimoto bosonization [11] (also see [12] and references therein), the highest-weight vector in C n λ 1 (z) is given by…”

Consistently constrained SL(N) WZWN models and classical exchange algebra

“…SL(N ) conformal primaries were discussed by the free field realization [4,10,12] of the current algebra of the WZWN model in [11,13]. We present the arguments of [13] in appendix A.…”

A slab Xe laser excited by a non-self-sustained discharge

“…Here, we just mention two of them: the Wakimoto construction (free field realization) [18][19][20] and the parafermion realization [21][22][23]. Recently, the explicit description of free field realizations of current algebras has been given in [24][25][26].…”