The taming of closed time-like curves

Rahul Biswas, Esko Keski-Vakkuri, Robert G. Leigh, Sean Nowling, Eric Sharpe

Research output: Contribution to journalArticlepeer-review


We consider a ℝ1,d/ℤ2 orbifold, where ℤ2 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 ℝ1,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.

Original languageEnglish (US)
Pages (from-to)1649-1679
Number of pages31
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 1 2004


  • Bosonic Strings
  • Discrete and Finite Symmetries
  • Renormalization Regularization and Renormalons

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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