On the Relationship between Discrete and Continuous Energy Spectra of SU(N) Supermembrane Matrix Model

TL;DR

This paper explores the connection between discrete and continuous energy spectra in the SU(N) supermembrane matrix model, suggesting that the existence of normalizable eigenstates implies a continuous spectrum for each partition of N.

Contribution

It demonstrates that assuming normalizable eigenstates exist, then a continuous energy spectrum branch must exist for each partition of N in the model.

Findings

Existence of a continuous spectrum branch for each N partition

Normalizable eigenstates imply continuous spectrum presence

Supports conjecture of normalizable eigenstates in the model

Abstract

It has been known that SU(N) supermembrane matrix model has continuous energy spectrum, and it has also been conjectured that it has a normalizable energy eigenstate. Assuming that there exists a normalizable energy eigenstate for each N, we show that there exists a branch of continuous energy spectrum for each partition of N.