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One-loop Evolution of a Rolling Tachyon

Xingang Chen

TL;DR

The paper investigates the time evolution of the one-loop cylinder in Sen's rolling tachyon background using the BCFT boundary state formulation. It demonstrates that in the long-cylinder limit the one-loop amplitude grows rapidly at late times, driven by timelike oscillator modes in the boundary state, which implies significant closed-string production and a possible breakdown of the rolling tachyon solution unless back-reaction is taken into account. By isolating contributions from the oscillator-free sector and the rest, the author shows the growth persists despite convergence of the primaries sum, highlighting the need for incorporating back-reaction and a physical time cutoff. The work also explores closed-string emission and a configuration with a spectator brane, indicating potential open-string production on the stable brane and illustrating how energy transfer between open and closed strings governs the decay dynamics. Overall, the results underscore the importance of quantum corrections in tachyon condensation and provide a framework for assessing back-reaction and multi-channel emission in brane decay scenarios.

Abstract

We study the time evolution of the one-loop diagram in Sen's rolling tachyon background. We find that at least in the long cylinder case they grow rapidly at late time, due to the exponential growth of the timelike oscillator terms in the boundary state. This can also be interpreted as the virtual open string pair creation in the decaying brane. This behavior indicates a breakdown of this rolling tachyon solution at some point during the evolution. We also discuss the closed string emission from this one-loop diagram, and the evolution of a one-loop diagram connecting a decaying brane to a stable brane, which is responsible for the physical open string creation on the stable brane.

One-loop Evolution of a Rolling Tachyon

TL;DR

The paper investigates the time evolution of the one-loop cylinder in Sen's rolling tachyon background using the BCFT boundary state formulation. It demonstrates that in the long-cylinder limit the one-loop amplitude grows rapidly at late times, driven by timelike oscillator modes in the boundary state, which implies significant closed-string production and a possible breakdown of the rolling tachyon solution unless back-reaction is taken into account. By isolating contributions from the oscillator-free sector and the rest, the author shows the growth persists despite convergence of the primaries sum, highlighting the need for incorporating back-reaction and a physical time cutoff. The work also explores closed-string emission and a configuration with a spectator brane, indicating potential open-string production on the stable brane and illustrating how energy transfer between open and closed strings governs the decay dynamics. Overall, the results underscore the importance of quantum corrections in tachyon condensation and provide a framework for assessing back-reaction and multi-channel emission in brane decay scenarios.

Abstract

We study the time evolution of the one-loop diagram in Sen's rolling tachyon background. We find that at least in the long cylinder case they grow rapidly at late time, due to the exponential growth of the timelike oscillator terms in the boundary state. This can also be interpreted as the virtual open string pair creation in the decaying brane. This behavior indicates a breakdown of this rolling tachyon solution at some point during the evolution. We also discuss the closed string emission from this one-loop diagram, and the evolution of a one-loop diagram connecting a decaying brane to a stable brane, which is responsible for the physical open string creation on the stable brane.

Paper Structure

This paper contains 12 sections, 56 equations, 2 figures.

Table of Contents

  1. introduction
  2. Review of Sen's description
  3. Spacelike One-loop
  4. One-loop evolution
  5. One-loop for rolling tachyon
  6. Closed string emission
  7. Adding a spectator brane
  8. Conclusion
  9. One-point functions on an Euclidean cylinder
  10. DD boundary conditions
  11. DN boundary conditions
  12. Closed string emission from one-loop

Figures (2)

  • Figure 1: The solid lines represents a cylinder of length $2\pi s$ and the circumference $2\pi$. The left and right vertical boundaries are to be identified. Here both horizontal boundaries satisfy the Dirichlet boundary condition. The vertex operator is inserted at $w$. The extended diagram including the dash lines and the image of the vertex operator is the equivalent torus. The "$+$" and "$-$" signs represent the charges of the sources.
  • Figure 2: Here the upper horizontal solid line represents Neumann boundary, and the lower one represents Dirichlet boundary. They give different image charges.