Schwinger-Dyson Equations of Matrix Models for Open and Closed Strings

TL;DR

This paper investigates the Schwinger-Dyson equations in a matrix model that describes open and closed string theories, revealing how the free energy relates to pure closed string models through source background adjustments.

Contribution

It demonstrates that the free energy with sources in an open-closed string matrix model satisfies Virasoro constraints similar to pure closed strings, connecting open and closed string formulations.

Findings

The free energy obeys Virasoro conditions akin to pure closed strings.

Background source values link open-closed and closed string models.

The approach extends understanding of string interactions via matrix models.

Abstract

We study the Schwinger-Dyson equations of a matrix model for an open-closed string theory. The free energy with source terms for scaling operators satisfies the same Virasoro conditions as those of the pure closed string and is obtained from that of the pure closed string by giving appropriate nonvanishing background values to all of the sources.