Mapping Tachyon effective field theory to a subsector of Klein-Gordon theory
On an unstable D-brane, the rolling of the tachyon away from the maximum of its potential is described by time-dependent solutions in string theory. Subsequent analysis leads to an understanding of physics around the tachyon vacuum in terms of an effective field theory. The classical solutions of this effective field theory in the late time limit are in one-to-one correspondence with configurations of non-rotating, non-interacting dust particles. In this work, we map this effective theory near the minimum of the potential to a consistent quantum description using collective field theory methods. The Hilbert space description we obtain in this way consists of a coherent state of particles at rest and excitations on top, i.e., a subsector of Klein-Gordon theory. This is in accordance with known results where one considers a decaying D-brane as providing a time-dependent source for closed strings, and the final closed string state produced is a coherent state. It also suggests, at the quantum level, an equivalence between the open string description and the closed string description regarding the decay of an unstable D-brane.