Strings in an electric field, and the Milne Universe

TL;DR

This paper investigates whether twisted string states can resolve the Milne Universe's spacelike singularity by analogy with charged strings in an electric field, revealing that twisted sectors contain physical states and are produced via the Schwinger mechanism.

Contribution

It demonstrates that twisted sectors in the Milne orbifold contain physical scattering states and can be produced through the Schwinger mechanism, challenging previous assumptions.

Findings

Twisted sectors contain physical scattering states.

Correlated pairs of twisted states are produced via Schwinger mechanism.

Open strings in electric fields serve as a useful model for time-dependent string phenomena.

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.