Closed Strings in Misner Space: Cosmological Production of Winding Strings

TL;DR

The paper analyzes closed strings in Misner space, a cosmological Lorentzian orbifold, by studying untwisted and twisted sectors, one-loop amplitudes, and back-reaction from winding strings. It develops a framework in which twisted strings resemble charged particles in an electric field, yielding short and long winding strings with distinct classical and quantum properties and showing tunneling-induced pair production. The one-loop amplitudes reveal divergences tied to Regge trajectories and Euclidean periodic orbits, while back-reaction from winding strings can induce a bounce and potentially regularize the singularity in low dimensions. Deformations of Milne/Grant spaces are proposed as means to tame large-winding production, suggesting a general mechanism by which stringy back-reaction can resolve cosmological pathologies in dynamical backgrounds.

Abstract

Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one of the simplest examples of a cosmological singularity in string theory. In this work, the study of weakly coupled closed strings on this space is pursued in several directions: (i) physical states in the twisted sectors are found to come in two kinds: short strings, which wind along the compact space-like direction in the cosmological (Milne) regions, and long strings, which wind along the compact time-like direction in the (Rindler) whiskers. The latter can be viewed as infinitely long static open strings, stretching from Rindler infinity to a finite radius and folding back onto themselves. (ii) As in the Schwinger effect, tunneling between these states corresponds to local pair production of winding strings. The tunneling rate approaches unity as the winding number $w$ gets large, as a consequence of the singular geometry. (iii) The one-loop string amplitude has singularities on the moduli space, associated to periodic closed string trajectories in Euclidean time. In the untwisted sector, they can be traced to the combined existence of CTCs and Regge trajectories in the spectrum. In the twisted sectors, they indicate pair production of winding strings. (iv) At a classical level and in sufficiently low dimension, the condensation of winding strings can indeed lead to a bounce, although the required initial conditions are not compatible with Misner geometry at early times. (v) The semi-classical analysis of winding string pair creation can be generalized to more general (off-shell) geometries. We show that a regular geometry regularizes the divergence at large winding number.

Figures (1)

• Figure 1: Cosmological flow in the presence of a condensate of winding strings along direction $i$, for $D=3, \mu=1/2$. The axes denote the Hubble parameters of the compact direction $i$ and non-compact directions $j$ in 11D Einstein frame. The dark blue line is the vanishing locus for the Hubble parameter of the direction $i$ in 10D string frame, i.e. $H_i + (H_k/2)=0$. The purple line is the vanishing locus for the Hubble parameter for the 11th direction $H_k$, obtained from Eq. (5.14). The trajectory shown in black corresponds to a bounce of the compact direction $i$ both in 11D Einstein and 10D string frame. It asymptotes to the clear blue line, corresponding to the fixed point $O$.