Bosonized Wakimoto Construction in the Principal Gradation

Abstract

It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra $\widehat g$, with arbitrary level k in the homogeneous gradation, in terms of dim$\left( g \right)$ free bosonic fields.However, its extension in the principal gradation has been achieved only in the simplest case k=1. In this Letter we show, in the case of the simplest affine algebra $\widehat{{\text{sl(2)}}}$,that the bosonized Wakimoto realization can be extended to the principal gradation only when k is equal to the critical level, i.e., –2.In this case, this construction can be achieved in terms ofarbitrary number (larger than 1) of free bosonic fields.