D-brane decay in two-dimensional string theory

We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [36] multiplied by the Neumann boundary state for the time coordinate t. In the dual description in terms of the c=1 matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [25], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for t which describes D0-brane decay.