Rolling Tachyon

TL;DR

This paper constructs and analyzes classical time-dependent solutions describing tachyon dynamics on unstable D-branes in open string theory, revealing their asymptotic behavior and boundary state properties.

Contribution

It provides a detailed construction of time-dependent tachyon solutions in string field theory, including boundary conformal field theory descriptions and boundary states.

Findings

Energy momentum tensor approaches a finite limit for certain tachyon evolutions.

Solutions exhibit singularities when the tachyon is pushed towards unbounded potential regions.

The study clarifies the boundary state structure of these time-dependent solutions.

Abstract

We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time derivatives, and hence it is not a priori clear how to set up the initial value problem, the theory contains a family of time dependent solutions characterized by the initial position and velocity of the tachyon field. We write down the world-sheet action of the boundary conformal field theories associated with these solutions and study the corresponding boundary states. For D-branes in bosonic string theory, the energy momentum tensor of the system evolves asymptotically towards a finite limit if we push the tachyon in the direction in which the potential has a local minimum, but hits a singularity if we push it in the direction where the potential is unbounded from below.