Coulomb Branch of the Lorentzian Three Algebra Theory

TL;DR

This paper investigates the Coulomb branch of a Lorentzian three algebra theory proposed for multiple M2-branes, demonstrating its consistency with expected physical properties and suggesting methods for further consistency testing.

Contribution

It provides an analysis of the Coulomb branch structure ensuring ghost decoupling and correct moduli space, advancing the understanding of this non-unitary M2-brane candidate.

Findings

The Coulomb branch structure is consistent with decoupling of ghost fields.

The physical moduli space matches that of multiple M2-branes.

A systematic procedure for testing theory consistency via higher derivative corrections.

Abstract

We analyze the coulomb branch of the non-unitary Lorentzian three algebra theory that has been proposed as a possible candidate for describing the world volume theory of multiple M2-branes. In order that it describes the theory of multiple M2-branes in flat eleven dimensional space-time, the ghost fields must decouple and the physical theory must be independent of the eight coordinates of the moduli space representing the center of mass coordinates of the branes. We show that the structure of the Coulomb branch is consistent with this requirement. While the full moduli space has the structure of a Lorentzian space modded out by a Lorentz transformation, the physical subspace has the correct structure of the moduli space of multiple M2-branes. We also suggest a systematic procedure for testing the consistency of the theory by computing the higher derivative corrections to the effective action obtained by integrating out the massive modes propagating in the loop.