D-brane Decay in Two-Dimensional String Theory

TL;DR

This paper analyzes the decay of unstable D0-branes in two-dimensional string theory using the dual matrix model, describing the process as an eigenvalue rolling down a potential and relating it to a coherent tachyon state.

Contribution

It provides a detailed dual description of D-brane decay in terms of matrix eigenvalues and fermionic states, connecting boundary states with coherent tachyon states.

Findings

Eigenvalue rolling models D-brane decay.

Coherent tachyon states match disk one-point functions.

Dual matrix model captures decay dynamics accurately.

Abstract

We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [hep-th/0101152] 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 [hep-th/0304224], 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.