Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum

Abstract

We present a novel supersymmetric Lorentz-covariant matrix model for M2-branes in M-theory, constructed via the framework of Restricted Volume-Preserving Deformations (RVPD) which is a residual symmetry from gauge-fixed volume-preserving diffeomorphisms. The model reformulates the supermembrane action entirely in terms of Nambu brackets, whose decomposition into Poisson brackets allows for a consistent matrix regularization that preserves both the Fundamental Identity and Lorentz covariance. Under the RVPD gauge structure, $κ$-symmetry is reduced to a restricted form ($\tildeκ$) that closes with RVPD transformations into a novel symmetry algebra. This algebra enables a systematic classification of BPS configurations: particle states (1/2-BPS), noncommutative membranes (1/4-BPS), and extended configurations in 4, 6, and 8 dimensions (1/8-, 1/16-, and 1/32-BPS), while the 10-dimensional case is non-BPS. The construction provides a natural lift of D2-brane matrix theory to M-theory and offers a pathway toward Lorentz-covariant matrix models for higher branes such as M5-branes.