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.

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

References in corpus (16)

• M Theory As A Matrix Model: A Conjecture
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• A Large-N Reduced Model as Superstring
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• On Foundation of the Generalized Nambu Mechanics
• On the Quantization of Nambu Brackets
• Deformation Quantization and Nambu Mechanics
• M theory as a matrix extension of Chern-Simons theory
• Volume Preserving Diffeomorphism and Noncommutative Branes
• On a Lorentz covariant matrix regularization of membrane theories
• Comments on the Problem of a Covariant Formulation of Matrix Theory
• Generalized Hamilton-Jacobi theory of Nambu Mechanics
• Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum