Boundary states as exact solutions of (vacuum) closed string field theory

We show that the boundary states are idempotent B*B=B with respect to the star product of HIKKO type closed string field theory. Variations around the boundary state correctly reproduce the open string spectrum with the gauge symmetry. We explicitly demonstrate it for the tachyonic and massless vector modes. The idempotency relation may be regarded as the equation of motion of closed string field theory at a possible vacuum.Comment: 30 pages, 2 figures, v3:regularization improve