The <f><ovl type="circ" STYLE="S">su</ovl>(2)−1/2</f> WZW model and the <f>βγ</f> system

The bosonic <f>βγ</f> 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 <f><ovl type="circ" STYLE="S">su</ovl>(2)−1/2</f> structure—of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this <f>βγ</f> 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 <f><ovl type="circ" STYLE="S">su</ovl>(2)−1/2</f> 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. [Copyright &y& Elsevier]