Eleven-dimensional Lorentz symmetry from SUSY quantum mechanics

The supermembrane in light-cone gauge gives rise to a supersymmetric quantu m mechanics system with SU(N) gauge symmetry when the group of area preserv ing diffeomorphisms is suitably regulated. de Wit, Marquard and Nicolai sho wed how eleven-dimensional Lorentz generators can be constructed from these degrees of freedom at the classical level. In this paper, these considerat ions are extended to the quantum level and it is shown the algebra closes t o leading nontrivial order at large N. A proposal is made for extending the se results to Matrix theory by realizing longitudinal boosts as large N ren ormalization group transformations.