Time Dependent Solution in Cubic String Field Theory

TL;DR

This paper investigates time-dependent solutions in cubic open string field theory related to the rolling tachyon, analyzing their behavior through numerical and analytical methods focusing on mode coefficients and large-time dynamics.

Contribution

It introduces a detailed numerical and analytical study of mode coefficients in truncated cubic string field theory, revealing unique large-n behaviors and their implications for tachyon dynamics.

Findings

Mode coefficients exhibit a (-β)^n λ^{-n^2} dependence with peaks at n=2^m.

Large-time behavior characterized by specific mode patterns.

Analytical solutions confirm numerical observations.

Abstract

We study time dependent solutions in cubic open string field theory which are expected to describe the configuration of the rolling tachyon. We consider the truncated system consisting of component fields of level zero and two, which are expanded in terms of cosh n x^0 modes. For studying the large time behavior of the solution we need to know the coefficients of all and, in particular, large n modes. We examine numerically the coefficients of the n-th mode, and find that it has the leading n-dependence of the form (-\beta)^n \lambda^{-n^2} multiplied by a peculiar subleading part with peaks at n=2^m=4,8,16,32,64,128,.... This behavior is also reproduced analytically by solving simplified equations of motion of the tachyon system.