String Field Theory Vertices, Integrability and Boundary States

We study Neumann coefficients of the various vertices in the Witten’s open string field theory (SFT). We show that they are not independent, but satisfy an infinite set of algebraic relations. These relations are identified as so-called Hirota identities. Therefore, Neumann coefficients are equal to the second derivatives of tau-function of dispersionless Toda Lattice hierarchy (this tau-function is just a partition sum of normal matrix model). As a result, certain two-vertices of SFT are identified with the Neumann boundary states on an arbitrary curve. We further analyze a class of SFT surface states, which can be re-written in the closed string language in terms of boundary states. This offers a new correspondence [email protected] On leave of absence from Bogolyubov ITP, Kiev, Ukraine [email protected] [email protected] 1 between open string states and closed string states (boundary states) in SFT. We conjecture that these special states can be considered as describing D-branes and other extended objects as ”solitons” in SFT. We consider some explicit examples, one of them is a surface states corresponding to orientifold.