c = 1 matrix model from string field theory

We show that the boundary string field theory (BSFT) on unstable D0-branes in 2d string theory is equivalent to the double scaled c = 1 matrix model (i.e. quadratic action), even though we naively expect many interaction terms in BSFT. It is checked that S-matrices are trivial in the open string theory on the D0-branes. We discuss how to take the closed string decoupling limit in our model in order to make its holographic interpretation clear. We also find some useful lessons from our results in 2d string toward the further understanding of the higher dimensional BSFT action