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<p>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, <i>κ</i>-symmetry is reduced to a restricted form <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27168_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <mover accent="true"> <mi>κ</mi> <mo stretchy="true">~</mo> </mover> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \left(\overset{\sim }{\kappa}\right) \)</EquationSource> </InlineEquation> 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.</p>

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Supersymmetric M2-brane matrix model with restricted volume-preserving deformations: Lorentz covariance and BPS spectrum

  • 期刊论文

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  • 发表日期：

    2025年9月10日

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  • So Katagiri

摘要

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 κ ~ \( \left(\overset{\sim }{\kappa}\right) \) 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.