On the unitarity of gauged non-compact WZNW strings

In this paper we investigate the unitarity of gauged non-compact WZNW strings, i.e., string theories formulated as G/H^′$G/H^{\prime }$ WZNW models, where G   is a non-compact group. These models represent string theories on non-trivial curved space–times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H^′$H^{\prime }$. The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.