Integrable Structures in String Field Theory

Abstract

We give a simple proof that the Neumann coefficients of surface states in Witten's 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.

11 pages; v.2:some adjustments, some explicit equations added

References in corpus (2)

• Integrability in SFT and new representation of KP tau-function
• N=(1|1) supersymmetric dispersionless Toda lattice hierarchy

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• Ghost story. III. Back to ghost number zero
• Light-cone Superstring Field Theory, pp-wave background and integrability properties
• On dispersionless coupled modified KP hierarchy
• Quasi-classical DBAR-dressing approach to the weakly dispersive KP hierarchy
• Kernel Formula Approach to the Universal Whitham Hierarchy