Integrability in SFT and new representation of KP tau-function

TL;DR

This paper explores the connection between conformal transformations in free boson CFTs and tau-functions of dispersionless KP hierarchies, with applications to string field theory and new representations of these tau-functions.

Contribution

It establishes a novel link between boundary states in free boson CFT and tau-functions of integrable hierarchies, providing a new representation and insights for string field theory.

Findings

Transformed vacuum states are expressed as tau-functions of dispersionless KP hierarchies.

Neumann coefficients correspond to second derivatives of tau-functions.

Surface states are identified with conformally transformed vacua.

Abstract

We are investigating the properties of vacuum and boundary states in the CFT of free bosons under the conformal transformation. We show that transformed vacuum (boundary state) is given in terms of tau-functions of dispersionless KP (Toda) hierarchies. Applications of this approach to string field theory is considered. We recognize in Neumann coefficients the matrix of second derivatives of tau-function of dispersionless KP and identify surface states with the conformally transformed vacuum of free field theory.