Algebraic Structure in 0<c<1 Open-Closed String Field Theories

TL;DR

This paper develops an algebraic framework for open-closed string field theories using stochastic quantization of matrix-vector models, revealing structures like Virasoro and SU(r) algebras in the continuum limit.

Contribution

It introduces a novel algebraic structure in open-closed string field theories derived from stochastic quantization of Kostov's models.

Findings

Identification of Virasoro algebra in the continuum Hamiltonian

Discovery of SU(r) current algebra in the string field theory

Derivation of an orientable open-closed string field theory at double scaling limit

Abstract

We apply stochastic quantization method to Kostov's matrix-vector models for the second quantization of orientable strings with Chan-Paton like factors, including both open and closed strings. The Fokker-Planck hamiltonian deduces an orientable open-closed string field theory at the double scaling limit. There appears an algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a SU(r) current algebra.