The ground state of the D=11 supermembrane and matrix models on compact regions

TL;DR

This paper develops a framework to analyze boundary value problems for matrix models at zero energy, proving existence and uniqueness of ground states for the D=11 supermembrane and related matrix models on finite regions.

Contribution

It introduces a general method to establish ground state properties for supersymmetric matrix models on compact regions, leveraging Dirichlet forms and supersymmetry.

Findings

Existence of ground state wavefunctions on finite regions.

Uniqueness of these ground states.

Framework applicable to D=11 supermembrane and SU(N) matrix models.

Abstract

We establish a general framework for the analysis of boundary value problems of matrix models at zero energy on compact regions. We derive existence and uniqueness of ground state wavefunctions for the mass operator of the $D=11$ regularized supermembrane theory, that is the $\mathcal{N}=16$ supersymmetric $SU(N)$ matrix model, on balls of finite radius. Our results rely on the structure of the associated Dirichlet form and a factorization in terms of the supersymmetric charges. They also rely on the polynomial structure of the potential and various other supersymmetric properties of the system.