Rolling Tachyon

TL;DR

The paper demonstrates the existence of time-dependent rolling tachyon solutions on unstable D-branes within open string field theory by exploiting a universal subspace and an exact marginal deformation, yielding a two-parameter family characterized by the initial position and velocity of the tachyon. It connects the space-time evolution to a solvable boundary conformal field theory and derives the corresponding boundary state, showing that energy remains localized on the D-brane plane rather than radiating into the bulk. An effective field theory analysis with electric flux reveals that decay products stay in the brane plane and cannot decouple from the flux dynamics, supporting a localized decay picture. The results illuminate how tachyon condensation proceeds in bosonic and (partially) in superstring settings and open avenues for further study in BCFT, vacuum string field theory, and cosmological applications of tachyon dynamics.

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.