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D-branes in a Big Bang/Big Crunch Universe: Misner Space

Yasuaki Hikida, Rashmi R. Nayak, Kamal L. Panigrahi

TL;DR

The paper investigates D-branes in Misner space, a time-dependent Lorentzian orbifold with a big bang/crunch singularity, by computing annulus amplitudes and boundary-state overlaps for D0 and D1 branes. The time dependence induces imaginary parts in the amplitudes, interpreted as open-string pair creation for localized D0 branes and winding closed-string emission for wrapping D1 branes; superstring analyses confirm these instabilities are not tied to tachyons. Correlation-function analyses show open-string amplitudes are less singular than their closed-string counterparts, yet singularities persist due to twisted-sector dynamics. Extending to Grant space, with an extra translational direction, suppresses many of these instabilities, yielding milder or resolved divergences in several amplitudes and suggesting a path toward more stable time-dependent backgrounds. Overall, the work uses boundary-state methods to illuminate stringy processes in cosmological backgrounds and highlights the crucial role of twisted sectors and background flux in brane dynamics near cosmological singularities.

Abstract

We study D-branes in a two-dimensional Lorentzian orbifold R^{1,1}/Γwith a discrete boost Γ. This space is known as Misner or Milne space, and includes big crunch/big bang singularity. In this space, there are D0-branes in spiral orbits and D1-branes with or without flux on them. In particular, we observe imaginary parts of partition functions, and interpret them as the rates of open string pair creation for D0-branes and emission of winding closed strings for D1-branes. These phenomena occur due to the time-dependence of the background. Open string 2 -> 2 scattering amplitude on a D1-brane is also computed and found to be less singular than closed string case.

D-branes in a Big Bang/Big Crunch Universe: Misner Space

TL;DR

The paper investigates D-branes in Misner space, a time-dependent Lorentzian orbifold with a big bang/crunch singularity, by computing annulus amplitudes and boundary-state overlaps for D0 and D1 branes. The time dependence induces imaginary parts in the amplitudes, interpreted as open-string pair creation for localized D0 branes and winding closed-string emission for wrapping D1 branes; superstring analyses confirm these instabilities are not tied to tachyons. Correlation-function analyses show open-string amplitudes are less singular than their closed-string counterparts, yet singularities persist due to twisted-sector dynamics. Extending to Grant space, with an extra translational direction, suppresses many of these instabilities, yielding milder or resolved divergences in several amplitudes and suggesting a path toward more stable time-dependent backgrounds. Overall, the work uses boundary-state methods to illuminate stringy processes in cosmological backgrounds and highlights the crucial role of twisted sectors and background flux in brane dynamics near cosmological singularities.

Abstract

We study D-branes in a two-dimensional Lorentzian orbifold R^{1,1}/Γwith a discrete boost Γ. This space is known as Misner or Milne space, and includes big crunch/big bang singularity. In this space, there are D0-branes in spiral orbits and D1-branes with or without flux on them. In particular, we observe imaginary parts of partition functions, and interpret them as the rates of open string pair creation for D0-branes and emission of winding closed strings for D1-branes. These phenomena occur due to the time-dependence of the background. Open string 2 -> 2 scattering amplitude on a D1-brane is also computed and found to be less singular than closed string case.

Paper Structure

This paper contains 29 sections, 212 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Closed strings in Misner space
  3. Closed strings in the twisted sectors
  4. Torus amplitude
  5. No-ghost theorem
  6. D-branes and annulus amplitudes
  7. Classical analysis on D-branes
  8. Localized D-brane
  9. Annulus amplitude
  10. Boundary state
  11. Open string pair creation
  12. Wrapping D-brane
  13. Annulus amplitude
  14. Boundary state
  15. Emission of winding closed strings
  16. ...and 14 more sections

Figures (2)

  • Figure 1: (A) D0-brane travels from infinite past to infinite future by passing a whisker region. (B) D1-brane covers the whole Misner space with or without flux on it.
  • Figure 2: The imaginary part of the cylinder amplitude may be interpreted as the rate of open string pair creation or/and closed string emission from the optical theorem. We identify that the imaginary part for open strings on the D0-brane is due to open string pair creation, and that for open strings on the D1-brane is due to emission of winding closed strings.