Dynamics and Stability of Light-Like Tachyon Condensation

TL;DR

This paper investigates the nonlinear dynamics and stability of light-like tachyon condensation in string theory, revealing conditions for stable evolution and the existence of an 'island of stability' in initial data space.

Contribution

It provides a detailed analysis of the initial value problem for light-like tachyon condensation, demonstrating stability properties in string field theory and p-adic string models through numerical and analytical methods.

Findings

For p-adic strings, stability depends on initial conditions.

String field theory exhibits complete stability for generic initial data.

An 'island of stability' exists in initial condition space.

Abstract

Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and nonperturbative vacua, without undergoing the wild oscillations that plague time-like solutions. In their analysis, however, the full structure of the initial value problem for the nonlocal dynamical equations was not considered. In this paper, therefore, we reexamine the nonlinear dynamics of light-like tachyon condensation using a combination of numerical and analytical techniques. We find that for the p-adic string the monotonic behaviour obtained previously relied on a special choice of initial conditions near the unstable maximum. For generic initial conditions the wild oscillations come back to haunt us. Interestingly, we find an "island of stability" in initial condition space that leads to sensible evolution at late times. For the string field theory case, on the other hand, we find that the evolution is completely stable for generic choices of initial data. This provides an explicit example of a string theoretic system that admits infinitely many initial data but is nevertheless nonperturbatively stable. Qualitatively similar dynamics are obtained in nonlocal cosmologies where the Hubble damping plays a role very analogous to the dilaton gradient.