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arXiv · 2509.23853

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

So Katagiri
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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.

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So Katagiri. 2026-01-29. Quantum Stability at One Loop for BPS Membranes in a Lorentz-Covariant RVPD Matrix Model. https://doi.org/10.1016/j.nuclphysb.2026.117516

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