Strings in an electric field, and the Milne Universe

TLDR: In this paper, it was shown that twisted sectors do contain physical scattering states, which can be viewed as charged particles in an electric field, and correlated pairs of twisted states will therefore be produced by the ordinary Schwinger mechanism.

Abstract: Arguably the simplest model of a cosmological singularity in string theory, the Lorentzian orbifold 1,1/boost is known to lead to severe divergences in scattering amplitudes of untwisted states, indicating a large backreaction towards 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 string scattering states of the Milne orbifold continue to non-normalizable modes in an unusual Euclidean orbifold of 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.