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

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

May 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..39.2971b&link_type=abstract

Physical Review D (Particles and Fields), Volume 39, Issue 10, 15 May 1989, pp.2971-2986

Statistics

17

Supergravity, Supersymmetry

Scientific paper

In a series of two papers we will generalize the extended Sugawara construction to the superalgebra SU(M+1||N+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.

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