Closed Timelike Curves and Holography in Compact Plane Waves

We discuss plane wave backgrounds of string theory and their relation to Gödel–like universes. This involves a twisted compactification along the direction of propagation of the wave, which induces closed timelike curves. We show, however, that no such curves are geodesic. The particle geodesics and the preferred holographic screens we find are qualitatively different from those in the Gödel–like universes. Of the two types of preferred screen, only one is suited to dimensional reduction and/or T–duality, and this provides a “holographic protection” of chronology. The other type of screen, relevant to an observer localized in all directions, is constructed both for the compact and non–compact plane waves, a result of possible independent interest. We comment on the consistency of field theory in such spaces, in which there are closed timelike (and null) curves but no closed timelike (or null) geodesics.