A Massive Study of M2-brane Proposals

TL;DR

This paper critically examines proposed worldvolume theories for M2-branes by analyzing their mass-deformed vacua, revealing discrepancies with predictions and supporting the ABJM theory's relevance through fuzzy three-sphere solutions.

Contribution

It provides the first detailed comparison of mass-deformed vacua in different M2-brane proposals, highlighting issues with the Lorentzian three-algebra theory and supporting ABJM theory.

Findings

Lorentzian three-algebra theory has only one classical vacuum.

ABJM theory exhibits more vacua than predicted, indicating a discrepancy.

Vacua in ABJM theory resemble fuzzy three-spheres, consistent with gravitational duals.

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.