WZNW Strings, Unitarity and Anti de Sitter spaces

We investigate the unitarity of strings on non-trivial space-time backgrounds based on gauged WZNW models involving SO(n,2), gauging an SO(n,1) subgroup. As geometric coset spaces, these are Anti de Sitter spaces. Our present models are more complicated than the ones considered previously, for example those connected to Hermitian symmetric spaces. In the present case, the time-like field component is not a center of the maximal compact subalgebra, leading to several additional complications. Assuming discrete representations, it will only be possible to consider n even, resulting in odd dimensional spaces. We will prove that such models are free of ghosts for a class of discrete representations.

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