On bosonization in BC system

A BC system follows the first order lagrangian based on the superconformal ghost which appears in BRST quantization in the superstring theory. It consists of a Grassmann-even superfield, B, with a superconformal weight of λ-1/2 and a Grassmann-odd super-field, C, with a superconformal weight of 1-λ. With respect to its components, a BC system consists of a fermion-ghost pair (b, c) and boson-ghost pair (β,γ), which are unified through supersymmetry. Thus, the bosonization is a BC system has conventionally been treated in terms of these two different pairs. Essentially, however, a BC system must be represented in such a supersymmetric form as (1,1). Super-Riemannian surfaces have to be considered in formulating the superstring theory. In general, therefore, non-split super-Riemannian surfaces have to be taken into account in performing superconformal transformation, and clear supersymmetry is important in considering a system on such non-split super-Riemannian surfaces. It is demonstrated here that there exists such bosonization (referred to as super-bosonization). In super-bosonization, a BC system is re-constructed by using vertex operators in two conjugate scalar super-fields connected with background charges. (Nogami, K.)