The su(2)-1/2 WZW model and the βγ system

The bosonic βγ ghost system has long been used in formal constructions of conformal field theory. It has become important in its own right in the last few years, as a building block of field theory approaches to disordered systems, and as a simple representative-due in part to its underlying su(2)-1/2 structure of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this βγ system, and uncover a number of striking features. We show, in particular, that the spectrum involves an infinite number of fields with arbitrarily large negative dimensions. These fields have their origin in a twisted sector of the theory, and have a direct relationship with spectrally flowed representations in the underlying su(2)-1/2 theory. We discuss the spectral flow in the context of the operator algebra and fusion rules, and provide a re-interpretation of the modular invariant consistent with the spectrum.