Algebraic Structure in Non-Orientable Open-Closed String Field Theories

TL;DR

This paper develops a non-orientable open-closed string field theory using stochastic quantization of matrix-vector models, revealing a new algebraic structure including Virasoro and SO(r) current algebras.

Contribution

It introduces a novel algebraic framework for non-orientable open-closed strings derived from matrix models via stochastic quantization.

Findings

Derives a well-defined string field theory at the double scaling limit.

Identifies a new algebraic structure in the continuum Fokker-Planck Hamiltonian.

Includes a Virasoro algebra and SO(r) current algebra in the model.

Abstract

We apply stochastic quantization method to real symmetric matrix-vector models for the second quantization of non-orientable strings, including both open and closed strings. The Fokker-Planck hamiltonian deduces a well-defined non-orientable open-closed string field theory at the double scaling limit of the matrix model. There appears a new algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a $SO(r)$ current algebra.