Integrable structures in string field theory

We give a simple proof that the Neumann coefficients of surface states in Wittenʹs SFT satisfy the Hirota equations for dispersionless KP hierarchy. In a similar way we show that the Neumann coefficients for the three string vertex in the same theory obey the Hirota equations of the dispersionless Toda Lattice hierarchy. We conjecture that the full (dispersive) Toda Lattice hierachy and, even more attractively a two–matrix model, may underlie open SFT.