Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding

TL;DR

This paper proves that the quantum Hamiltonian of the compactified D=11 supermembrane with non-trivial winding has a discrete spectrum, confirming its spectral discreteness through rigorous mathematical analysis.

Contribution

It provides a rigorous proof that the Hamiltonian of the supermembrane with non-trivial winding has a discrete spectrum, advancing understanding of its quantum properties.

Findings

Hamiltonian has compact resolvent

Spectrum consists of discrete eigenvalues

Finite multiplicity of eigenvalues

Abstract

We analyze the Hamiltonian of the compactified D=11 supermembrane with non-trivial central charge in terms of the matrix model constructed recently by some of the authors. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.