Octonionic twists for supermembrane matrix models

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.