The Taming of Closed Time-like Curves

Details The Taming of Closed Time-like Curves The Taming of Closed Time-like Curves

2003-04-28

arxiv.org/abs/hep-th/0304241v3

JHEP 0401:064,2004

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, LaTeX2e, uses amssymb, amsmath and epsf macros, 8 eps and 3 ps figures; (v2): Two additional comments + one referenc

Scientific paper

10.1088/1126-6708/2004/01/064

We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target space would be just the Minkowski space $R^{1,d}$, suggesting a zero result for the superstring. This leads us to propose a proper reformulation of QFT, and recalculate the stress tensor. We find almost the same result as in Minkowski space, except for a potential divergence at the initial time slice of the orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that it is possible to define local S-matrices, even if the spacetime is globally time-nonorientable.

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