Fermionic construction in the supersymmetric coset model

Abstract

It is known previously that the operator product expansion (OPE) between the first [Formula: see text] multiplet and itself contains the second [Formula: see text] multiplet in the supersymmetric coset model. In this paper, by using their realizations in terms of various fermions, we compute the four kinds of OPEs between the first and the second [Formula: see text] multiplets for fixed [Formula: see text] and [Formula: see text], where the group of the coset contains [Formula: see text]. By supersymmetrizing the above OPEs in [Formula: see text] superspace and using the various Jacobi identities between the currents, we determine the [Formula: see text] supersymmetric OPE between the first and the second [Formula: see text] multiplets completely. The right-hand side of this OPE contains the various [Formula: see text] multiplets: the [Formula: see text] singlet [Formula: see text] multiplets of superspin-[Formula: see text] and the [Formula: see text] triplet [Formula: see text] multiplets of superspin-[Formula: see text]. The [Formula: see text] superspace description and the decoupling of the spin-[Formula: see text] current of the [Formula: see text] superconformal algebra are also described.