Rolling Tachyon

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.

D-brane decay in two-dimensional string theory

“…Another general lesson is that the wavefunction of the open string modes gets imprinted in the final wave function for the closed strings. In this completely solvable example we find that the "tachyon matter" state introduced in [1] is just the state of closed strings that the brane decays into. Another interesting issue is the relation between the tachyon potentials discussed in the context of string field theory [46,47,48] to the simple inverted quadratic potential we find here.…”

“…whereλ = sin πλ andλ is the variable that appears in the description of the boundary state [1]. We finally get that the emission rate is…”

“…Sen's boundary state with parameterλ [1] corresponds, in the matrix model, to an eigenvalue that starts at the position y = − 2α µ sin πλ .…”

“…The spaces parameterized by them are related to each other through a nonlocal transform [41,53]. The time-dependence of an eigenvalue (the open string tachyon) does not describe motion of a D0-brane in φ; rather, it describes the decay of a D0-brane localized at large φ [1]. The time dependence in the φ description arises only from the boundary interaction (1.1).…”

“…In a series of seminal papers Sen proposed a boundary conformal field theory (BCFT) description of the decay of unstable D-branes [1,2,3]. In the bosonic string theory, the BCFT contains a boundary interaction…”