The boundary state from open string fields

We construct a class of BRST-invariant closed string states for any classical solution of open string field theory. The closed string state is a nonlinear functional of the open string field and changes by a BRST-exact term under a gauge transformation of the solution. As a result, its contraction with an on-shell closed string state provides a gauge-invariant observable of open string field theory. Unlike previously known observables, however, the contraction with off-shell closed string states in the Fock space is well defined and regular. Moreover, we claim that the BRST-invariant closed string state coincides, up to a possible BRST-exact term, with the boundary state of the boundary conformal field theory which the solution is expected to describe. Our construction requires a choice of a propagator strip. If we choose the Schnabl propagator strip, the BRST-invariant state becomes explicitly calculable. We calculate it for various known analytic solutions of open string field theory and, remarkably, we find that it precisely coincides with the boundary state without any additional BRST-exact term. Our results imply, in particular, that the wildly oscillatory rolling tachyon solution of open string field theory actually describes the regular closed string physics studied by Sen using the boundary state.