Eleven-Dimensional Lorentz Symmetry from SUSY Quantum Mechanics

TL;DR

This paper extends the classical construction of eleven-dimensional Lorentz symmetry from supermembrane quantum mechanics to the quantum level, demonstrating algebra closure at large N and proposing a method to incorporate boosts via renormalization group transformations.

Contribution

It advances the understanding of Lorentz symmetry realization in quantum supermembrane models and proposes a novel approach for extending these results to Matrix theory.

Findings

Lorentz algebra closes at quantum level for large N

Constructs Lorentz generators from supersymmetric quantum mechanics

Proposes realization of boosts as renormalization group transformations

Abstract

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