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The critical dimension of string theories in which the background metric is a product of Minkowski space and an SU(N) or SO(N) group manifold is derived. A consistent string theory can be constructed only in the presence of a Wess-Zumino term associated with the compactified dimension. This implies that the compactified radius is quantized in units of the string tension. A generalization to the supersymmetric case is discussed.
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Nemeschansky et al. (1985) studied this question.
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