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We show that boundary string field theory realizes the minimalmodel of open string field theory. More precisely, we observe that theexpansion of the (co)homological vector field, $Q$ of boundary string fieldtheory in the cohomology of its linear part reproduces the S-matrices ofperturbative string theory. In mathematical terms, boundary string field theoryrealizes the minimal model map of the cohomological perturbation lemma.

Classical Open String Amplitudes and Boundary String Field Theory