The WZNW model onPSU(1,1|2)

According to the work of Berkovits, Vafa and Witten (hep-th/9902098), thenon-linear sigma model on the supergroup PSU(1,1|2) is the essential buildingblock for string theory on AdS(3)xS(3)xT(4). Models associated with anon-vanishing value of the RR flux can be obtained through a psu(1,1|2)invariant marginal deformation of the WZNW model on PSU(1,1|2). We take this asa motivation to present a manifestly psu(1,1|2) covariant construction of themodel at the Wess-Zumino point, corresponding to a purely NSNS background3-form flux. At this point the model possesses an enhanced psu(1,1|2) currentalgebra symmetry whose representation theory, including explicit characterformulas, is developed systematically in the first part of the paper. The spaceof vertex operators and a free fermion representation for their correlationfunctions is our main subject in the second part. Contrary to a widespreadclaim, bosonic and fermionic fields are necessarily coupled to each other. Theinteraction changes the supersymmetry transformations, with drasticconsequences for the multiplets of localized normalizable states in the model.It is only this fact which allows us to decompose the full state space intomultiplets of the global supersymmetry. We analyze these decompositionssystematically as a preparation for a forthcoming study of the RR deformation.Comment: 59 pages, 2 figures, v2: a couple of typos corrected, in particular above eq. (2.26) the labels of the representations which decouple. The modifications have no affect on any of the formula