The Taming of Closed Time-like Curves

We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and spacereversal, also known as the embedding space of the elliptic de Sitter space.The background has two potentially dangerous problems: time-nonorientabilityand the existence of closed time-like curves. We first show that closed causalcurves disappear after a proper definition of the time function. We thenconsider the one-loop vacuum expectation value of the stress tensor. A naiveQFT analysis yields a divergent result. We then analyze the stress tensor inbosonic string theory, and find the same result as if the target space would bejust the Minkowski space $R^{1,d}$, suggesting a zero result for thesuperstring. This leads us to propose a proper reformulation of QFT, andrecalculate the stress tensor. We find almost the same result as in Minkowskispace, except for a potential divergence at the initial time slice of theorbifold, analogous to a spacelike Big Bang singularity. Finally, we argue thatit is possible to define local S-matrices, even if the spacetime is globallytime-nonorientable.Comment: 37 pages, LaTeX2e, uses amssymb, amsmath and epsf macros, 8 eps and 3 ps figures; (v2): Two additional comments + one reference added; (v3): corrections in discussion of CTCs + some clarification