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Dynamical Cobordism and the Beginning of Time: Supercritical Strings and Tachyon Condensation

Roberta Angius, Matilda Delgado, Angel M. Uranga

TL;DR

The paper reframes timelike linear dilaton backgrounds in supercritical strings as time-dependent Dynamical Cobordisms, identifying the spacelike beginning-of-time singularity with a boundary defined by an ETW brane. It establishes that both the timelike-dilaton onset and the lightlike tachyon wall exhibit the same critical exponent δ = 2/√{D-2}, suggesting a shared microscopic origin in strong-coupling closed tachyon condensation and linking to bubbles of nothing from lightlike tachyon condensation. Using an EFT with a tachyon-dependent function f1(T), the authors demonstrate the robustness of the ETW scaling across a broad class of f1 profiles, supporting a universal picture of the beginning-of-time resolution. The work proposes that the beginning of time is a cobordism boundary to nothing triggered by closed tachyon dynamics, with potential implications for other supercritical theories and for understanding cosmological singularities within the cobordism framework.

Abstract

We describe timelike linear dilaton backgrounds of supercritical string theories as time-dependent Dynamical Cobordisms in string theory, with their spacelike singularity as a boundary defining the beginning of time. We propose and provide compelling evidence that its microscopic interpretation corresponds to a region of (a strong coupling version of) closed tachyon condensation. We argue that this beginning of time is closely related to (and shares the same scaling behaviour as) the bubbles of nothing obtained in a weakly coupled background with lightlike tachyon condensation. As an intermediate result, we also provide the description of the latter as lightlike Dynamical Cobordism.

Dynamical Cobordism and the Beginning of Time: Supercritical Strings and Tachyon Condensation

TL;DR

The paper reframes timelike linear dilaton backgrounds in supercritical strings as time-dependent Dynamical Cobordisms, identifying the spacelike beginning-of-time singularity with a boundary defined by an ETW brane. It establishes that both the timelike-dilaton onset and the lightlike tachyon wall exhibit the same critical exponent δ = 2/√{D-2}, suggesting a shared microscopic origin in strong-coupling closed tachyon condensation and linking to bubbles of nothing from lightlike tachyon condensation. Using an EFT with a tachyon-dependent function f1(T), the authors demonstrate the robustness of the ETW scaling across a broad class of f1 profiles, supporting a universal picture of the beginning-of-time resolution. The work proposes that the beginning of time is a cobordism boundary to nothing triggered by closed tachyon dynamics, with potential implications for other supercritical theories and for understanding cosmological singularities within the cobordism framework.

Abstract

We describe timelike linear dilaton backgrounds of supercritical string theories as time-dependent Dynamical Cobordisms in string theory, with their spacelike singularity as a boundary defining the beginning of time. We propose and provide compelling evidence that its microscopic interpretation corresponds to a region of (a strong coupling version of) closed tachyon condensation. We argue that this beginning of time is closely related to (and shares the same scaling behaviour as) the bubbles of nothing obtained in a weakly coupled background with lightlike tachyon condensation. As an intermediate result, we also provide the description of the latter as lightlike Dynamical Cobordism.
Paper Structure (17 sections, 81 equations, 1 figure)

This paper contains 17 sections, 81 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Overview of Dynamical Cobordisms
  3. Supercritical strings as time-dependent Dynamical Cobordism
  4. Linear timelike dilaton as Dynamical Cobordism
  5. The ETW brane at the beginning of time
  6. The timelike tachyon case
  7. Lightlike tachyon condensation
  8. Lightlike tachyon in the worldsheet description
  9. Spacetime description and lightlike ETW brane
  10. Effective action
  11. The local scalings
  12. General $f_1$
  13. The strong coupling region and the origin of time
  14. Conclusions
  15. Dimension quenching as an interpolating domain wall
  16. ...and 2 more sections

Figures (1)

  • Figure 1: Depiction of a spacetime slice at which the solutions attain a large fixed field space distance in the tachyon-dilaton space. The asymptotes near $x^0\sim 0$ and $x^+\sim 0$, should be regarded as corresponding to the physical location of the ETW branes, which are hence recombined in the middle region, and which for a boundary of spacetime, with nothing beyond them. The spray line signal the location of the singularities.