Strings in an electric field, and the Milne Universe

Abstract

Arguably the simplest model of a cosmological singularity in string theory, the Lorentzian orbifold $\Real^{1,1}/boost$ is known to lead to severe divergences in scattering amplitudes of untwisted states, indicating a large backreaction toward the singularity. In this work we take a first step in investigating whether condensation of twisted states may remedy this problem and resolve the spacelike singularity. By using the formal analogy with charged open strings in an electric field, we argue that, contrary to earlier claims, twisted sectors do contain physical scattering states, which can be viewed as charged particles in an electric field. Correlated pairs of twisted states will therefore be produced, by the ordinary Schwinger mechanism. For open strings in an electric field, on-shell wave functions for the zero-modes are determined, and shown to analytically continue to non-normalizable modes of the usual Landau harmonic oscillator in Euclidean space. Closed strings scattering states of the Milne orbifold continue to non-normalizable modes in an unusual Euclidean orbifold of $\Real^2$ by a rotation by an irrational angle. Irrespective of the formal analogy with the Milne Universe, open strings in a constant electric field, or colliding D-branes, may also serve as a useful laboratory to study time-dependence in string theory.

46 pages, 8 figures, uses JHEP3.cls; v2: minor corrections, clarifications and several refs added; v3: more minor corrections, final version published in JCAP

References in corpus (4)

• Holographic Protection of Chronology in Universes of the Godel Type
• Pair production in a strong electric field: an initial value problem in quantum field theory
• Removing Singularities
• Relativistic String in a Pulse

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• Closed Strings in Misner Space: Stringy Fuzziness with a Twist
• Hagedorn transition and chronology protection in string theory
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• Winding String Condensation and Noncommutative Deformation of Spacelike Singularity
• String spectra near some null cosmological singularities
• D-branes in a Big Bang/Big Crunch Universe: Nappi-Witten Gauged WZW Model
• Closed strings in Misner space: a toy model for a Big Bounce ?
• Open Strings and Electric Fields in Compact Spaces