A Massive Study of M2-brane Proposals

TL;DR

This study tests two prominent M2-brane worldvolume proposals by examining maximally supersymmetric mass deformations. The ABJM-based deformation yields a discrete set of classical vacua with fuzzy $S^3$ characteristics, but the vacuum count exceeds the simple partition-based prediction, prompting proposed resolutions involving quantum effects or missing deformation terms. The BF membrane model fails at the classical level, displaying only a single vacuum and challenging its interpretation as the M2-brane theory. Collectively, the results reinforce the ABJM framework’s connection to M2–M5 physics through fuzzy sphere vacua while highlighting unresolved counting and quantum-consistency questions for multiple proposals.

Abstract

We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the mass-deformed theory on N M2-branes: that there should be a set of discrete vacua in one-to-one correspondence with partitions on N. For the mass-deformed Lorentzian three-algebra theory, we find only a single classical vacuum, casting doubt on its M2-brane interpretation. For the mass-deformed ABJM theory, we do find a discrete set of solutions, but these are more numerous than predicted. We discuss possible resolutions of this puzzling discrepancy. We argue that the classical vacuum solutions of the mass-deformed ABJM theory display properties of fuzzy three-spheres, as expected from their gravitational dual interpretation.