A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations
Abstract
We propose a Lorentz covariant matrix model as a nonperturbative formulation of the bosonic M2-brane in M-theory. Unlike previous approaches relying on the light-cone gauge or symmetry-based constructions, our model retains full 11-dimensional Lorentz invariance by introducing a novel gauge-fixing condition that restricts the symmetry of volume-preserving deformations (VPD) to a subclass, which we call restricted VPD (RVPD). This restriction enables a consistent matrix regularization of the Nambu bracket, bypassing the long-standing obstructions related to the Leibniz rule and the Fundamental Identity. The resulting model exhibits RVPD symmetry, admits particle-like and noncommutative membrane solutions, and lays the foundation for a Lorentz-invariant, nonperturbative matrix description of M2-branes. Our work offers a new paradigm for constructing Lorentz-invariant matrix models of membranes, revisiting the algebraic structure underlying M-theory.
Cite
@article{arxiv.2504.05940,
title = {A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations},
author = {So Katagiri},
journal= {arXiv preprint arXiv:2504.05940},
year = {2025}
}
Comments
31 pages, Minor revision: added a clarifying footnote on $C_I$, included the reference to the supersymmetric extension (now accepted in JHEP), and made minor textual corrections