USp(2k) Matrix Model: Schwinger-Dyson Equations and Closed-Open String Interactions

TL;DR

This paper derives Schwinger-Dyson equations for the USp(2k) matrix model, revealing interactions that correspond to nonorientable Type I superstrings and incorporating open string boundary conditions.

Contribution

It introduces a complete set of loop equations for the USp(2k) matrix model that include both closed and open string interactions, advancing understanding of nonorientable string theories.

Findings

Loop equations close among closed and open Wilson loops

Reveals joining and splitting interactions for nonorientable strings

Derives boundary conditions for open string loops

Abstract

We derive the Schwinger-Dyson/loop equations for the USp(2k) matrix model which close among the closed and open Wilson loop variables. These loop equations exhibit a complete set of the joining and splitting interactions required for the nonorientable Type I superstrings. The open loops realize the SO(2n_f) Chan-Paton factor and their linearized loop equations derive the mixed Dirichlet/Neumann boundary conditions.