Open-Closed String Duality, Branes, and Topological Recursion

TL;DR

This paper explores the duality between open and closed strings in matrix models, revealing how operator insertions relate to topological expansions, and connects topological recursion with branes through Virasoro constraints.

Contribution

It establishes a relationship between different classes of matrix models and their string equations, linking open-closed duality with topological recursion and brane correlation functions.

Findings

Mapped point-like operator insertions to open string free energy expansions

Computed correlation functions of macroscopic loops and FZZT branes

Analyzed Virasoro conditions to connect topological recursion with branes

Abstract

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the $\beta = 2$ Wigner-Dyson class and models in the $(1 + 2\Gamma, 2)$ Altland-Zirnbauer class relates the perturbative solutions of the two systems' string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.