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arXiv · 2504.05940

A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations

So Katagiri
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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.

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So Katagiri. 2025-08-27. A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations. https://doi.org/10.1142/s0217751x26500831

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