Extended Sugawara construction for the superalgebras SU(M+1chemical bondN+1). I. Free-field representation and bosonization of super Kac-Moody currents

In a series of two papers we will generalize the extended Sugawara construction to the superalgebra SU(M+1chemical bondN+1). This first part contains ground work which we need to construct examples of closed extended algebras. We develop the tensor analysis for contractions of super d and f symbols, and we present a free-field representation of the super Kac-Moody currents at level 1 in terms of spin-0 fields. This is obtained from the standard spin-1/2 conjugate free-field representation by bosonization. Because of the mixed statistics, some of these conjugate pairs are of the βγ type--similar to the superghosts appearing in Neveu-Schwarz-Ramond strings. The partial check on bosonization we carry out, in which we compare the torus partition functions before and after bosonization, is also of interest in that context