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A Lorentz covariant matrix model for bosonic M2-branes: Nambu brackets and restricted volume-preserving deformations.

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Bibliographic Details
Title: A Lorentz covariant matrix model for bosonic M2-branes: Nambu brackets and restricted volume-preserving deformations.
Authors: Katagiri, So1 (AUTHOR) So.Katagiri@gmail.com
Source: International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics. 5/10/2026, Vol. 41 Issue 13, p1-29. 29p.
Subjects: Branes, Diffeomorphisms, Supergravity
Abstract: In this paper, 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 (VPDs) 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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:In this paper, 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 (VPDs) 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. [ABSTRACT FROM AUTHOR]
ISSN:0217751X
DOI:10.1142/S0217751X26500831