WZNW Strings, Unitarity and Anti de Sitter spaces

TL;DR

This paper examines the unitarity of string theories on Anti de Sitter backgrounds modeled by gauged WZNW models, demonstrating ghost-free conditions for certain discrete representations in even-dimensional spaces.

Contribution

It extends previous work by analyzing more complex gauged WZNW models on AdS spaces with non-trivial algebraic structures, establishing unitarity conditions.

Findings

Models are ghost-free for specific discrete representations.

Unitarity holds in even-dimensional Anti de Sitter spaces.

Additional complications arise due to non-central time-like components.

Abstract

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.