Octonionic twists for supermembrane matrix models

TL;DR

This paper proves that a specific G_2×U(1) invariant Hamiltonian derived from the supermembrane matrix model has a spectrum covering all positive energies, potentially aiding in finding zero-energy states in the original model.

Contribution

It introduces an octonionic conjugation method to analyze the spectrum of a supermembrane matrix model variant, revealing its spectral properties.

Findings

Spectrum covers the entire positive half-axis

G_2×U(1) invariance established

Potential for identifying zero-energy states

Abstract

A certain G_2 times U(1) invariant Hamiltonian arising from the standard membrane matrix model via conjugating any of the supercharges by a cubic, octonionic, exponential is proven to have a spectrum covering the whole positive half-axis. The model could be useful in determining a normalizable zero-energy state in the original SO(9) invariant SU(N) matrix model.