Matrix Model for Dirichlet Open String

TL;DR

This paper explores the matrix model description of Dirichlet open strings ending on D-branes within the IKKT framework, focusing on boundary conditions, gauge choices, and specific dimensional reductions.

Contribution

It determines consistent boundary conditions for Green-Schwarz superstrings and connects the matrix regularization to super Yang-Mills theories for certain D-branes.

Findings

Boundary conditions compatible with supersymmetry and κ-symmetry are established.

In Schild gauge, the system describes limited dimensional D p-branes (p=3,7).

For p=3, the matrix model reduces to 6D N=1 super Yang-Mills.

Abstract

We discuss the open string ending on D $p$-branes in IKKT framework. First we determine the boundary conditions of Green-Schwarz superstring which are consistent with supersymmetry and $\kappa$-symmetry. We point out some subtleties arising from taking the Schild gauge and show that in this gauge the system incorporates the limited dimensional D $p$-branes ($p=3,7$). The matrix regularization for the Dirichlet open string is given by gauge group SO(N). When $p=3$, the matrix model becomes the dimensional reduction of a 6 dimensional ${\cal N}=1$ super Yang-Mills theory.