Quantum Stability at One Loop for BPS Membranes in a Lorentz-Covariant RVPD Matrix Model

2025/09/28 by Katagiri, So
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.23853

Abstract

We establish the first rigorous one-loop proof of quantum stability for BPS membranes in the Lorentz-covariant M2-brane matrix model with Restricted Volume-Preserving Deformations (RVPD). Exploiting the closure of restricted κ-symmetry with RVPD ensures that the BRST complex terminates without an infinite ghost tower, keeping the gauge-fixed measure analytically controllable. Our main result establishes that the 2D, 4D, 6D, and 8D noncommutative membranes remain stable, while the 10D configuration inevitably develops a tachyonic mode. Our analysis unifies the treatment of zero-modes, connects the effective action to central charges, and clarifies relations to BFSS, BLG/ABJM, and prospective M5-brane matrix models, providing a roadmap for RVPD-based extensions.

Citations

• Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
• A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations
• The M5-Brane Limit of Eleven-Dimensional Supergravity
• Shifted Symplectic Structures
• Towards Covariant Matrix Theory

Related

• A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations
• Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
• Membrane Matrix models and non-perturbative checks of gauge/gravity\n duality
• Rigid open membrane and non-abelian non-commutative Chern-Simons theory
• Near-extremal membranes in M-theory