Abstract :
We construct a string field Hamiltonian describing the dynamics of open and closed strings with effective target-space dimension c ≤ 1. In order to do so, we first derive the Dyson-Schwinger equations for the underlying large N vector+matrix model and formulate them as a set of constraints satisfying decoupled Virasoro and U(1) current algebras. The Hamiltonian consists of a bulk and a boundary term having different scaling dimensions. The time parameters corresponding to the two terms are interpreted from the the point of view of the fractal geometry of the world surface.
