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

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.

Latex, 26 pages. We have added some comments at the introduction in order to make it easier for the reader. Results of the paper unchanged

References in corpus (11)

• The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
• Classical trajectories and quantum supersymmetry
• Asymptotic Factorisation of the Ground-State for SU(N)-invariant Supersymmetric Matrix-Models
• Supersymmetry: Boundary Conditions and Edge States
• Towards the Ground State of the Supermembrane
• Massless ground state for a compact SU(2) matrix model in 4D
• On the groundstate of octonionic matrix models in a ball
• Boundary Effects in Bosonic and Fermionic Field Theories
• On the Ground State Wave Function of Matrix Theory
• On the Construction of Zero Energy States in Supersymmetric Matrix Models IV
• Spin(9) Average of SU(N) Matrix Models I. Hamiltonian

Cited by in corpus (5)

• Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities
• Massless ground state for a compact SU(2) matrix model in 4D
• Measure of the potential valleys of the supermembrane theory
• Existence of a Supersymmetric Massless Ground State of the $SU(N)$ Matrix Model globally on its Valleys
• Optimized Fock space in the large N limit of quartic interactions in Matrix Models