STRING PROPAGATION IN BACKGROUNDS WITH CURVED SPACE-TIME

We study propagation of bosonic strings and superstrings in background metrics with curved space-time using non-compact current algebras. We discuss 2 + 1 dimensional (super)strings on the SO(2,1) group manifold. Using a coset model we construct a (d - 1)+1 dimensional de Sitter (super)strings for d=2,3,4...10 or 26. We also discuss the posibility of a discrepancy in counting the number of time (i.e. non-compact) coordinates for the classical string versus the quantum string. We illustrate this with several examples. We show evidence that a string or superstring propagating in a background with curved time cannot be excited to arbitrarily high states and that it is unitary only in low lying states. We offer a possible interpretation of this phenomenon. © 1991.