A Matrix Model from String Field Theory

We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and a U(N) vector which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both in finite and large N. Increase of potential height is observed in both examples. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.