String Field Theory Vertices, Integrability and Boundary States

TL;DR

This paper reveals that Neumann coefficients in open string field theory satisfy Hirota identities, linking them to integrable hierarchies and boundary states, and proposes their interpretation as D-branes or solitons.

Contribution

It establishes a connection between string field theory vertices, integrability via Hirota identities, and boundary states, introducing a novel perspective on non-perturbative objects.

Findings

Neumann coefficients satisfy Hirota identities.

Neumann coefficients relate to the tau-function of dispersionless Toda hierarchy.

Certain surface states correspond to boundary states and D-branes.

Abstract

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 the partition sum of normal matrix model). As a result, certain two-vertices of SFT are identified with the boundary states, corresponding to boundary conditions on an arbitrary curve. Such two-vertices can be obtained by the contraction of special surface states with Witten's three vertex. We analyze a class of SFT surface states,which give rise to boundary states under this procedure. We conjecture that these special states can be considered as describing D-branes and other non-perturbative objects as "solitons" in SFT. We consider some explicit examples, one of them is a surface states corresponding to orientifold.