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.

Analytic solution for tachyon condensation in open string field theory

“…For the states (2.68), we may use the identities (see Appendix D.1) 71) and thanks to the fact that B 1 and (B 0 + B † 0 ) raise the L 0 eigenvalue by one, we can reduce this case to the previous one.…”

Universal Whitham hierarchy, dispersionless Hirota equations and multicomponent KP hierarchy

“…As (11) implies, differentiating (12) by z β (p) while leaving the time variables constant yields ζ 0 (p) and ζ β (p), which thus turns out to be Laurent series of the form…”

On the validity of the solution of string field theory

“…The complexity of this equation stems from the infinite number of string fields, its non-linearity and the difference in forms of the linear and nonlinear terms. Many attempts have been made in order to simplify the structure of this equation [3][4][5][6][7][8][9][10][11][12][13][14]. Approximate numerical solutions were found earlier using level truncation regularization [15].…”