The WZNW model on PSU(1,1|2)

TL;DR

This paper constructs a psu(1,1|2) covariant WZNW model at the Wess-Zumino point for string theory on AdS3xS3xT4, analyzing its symmetry, vertex operators, and supersymmetry structure, setting the stage for future RR flux deformations.

Contribution

It provides a systematic, covariant construction and analysis of the psu(1,1|2) WZNW model, including symmetry, representation theory, and vertex operators, at the pure NSNS flux point.

Findings

Developed explicit character formulas for the current algebra representations.

Showed that bosonic and fermionic fields are necessarily coupled.

Decomposed the state space into supersymmetric multiplets.

Abstract

According to the work of Berkovits, Vafa and Witten (hep-th/9902098), the non-linear sigma model on the supergroup PSU(1,1|2) is the essential building block for string theory on AdS(3)xS(3)xT(4). Models associated with a non-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 as a motivation to present a manifestly psu(1,1|2) covariant construction of the model at the Wess-Zumino point, corresponding to a purely NSNS background 3-form flux. At this point the model possesses an enhanced psu(1,1|2) current algebra symmetry whose representation theory, including explicit character formulas, is developed systematically in the first part of the paper. The space of vertex operators and a free fermion representation for their correlation functions is our main subject in the second part. Contrary to a widespread claim, bosonic and fermionic fields are necessarily coupled to each other. The interaction changes the supersymmetry transformations, with drastic consequences for the multiplets of localized normalizable states in the model. It is only this fact which allows us to decompose the full state space into multiplets of the global supersymmetry. We analyze these decompositions systematically as a preparation for a forthcoming study of the RR deformation.