Towards open–closed string duality: Closed Strings as Open String Fields

We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off–shell) level–matched closed string states are represented by star algebra projectors in open string field theory. Particular attention is paid to the zero mode sector, which is indispensable in order to generate closed string states with momentum. As an outcome of our identification, we show that boundary states, which in closed string theory represent D–branes, correspond to the identity string field in the open string side. It is to be remarked that closed string theory D–branes are thus given by an infinite superposition of star algebra projectors.