KK6 from M2 in BLG

TL;DR

This paper explores deriving the KK6 monopole world-volume action from multiple M2-branes described by BLG theory, highlighting the role of infinite-dimensional Lie 3-algebras and Nambu-Poisson structures.

Contribution

It proposes a novel approach to obtain KK6 from M2 using Nambu-Poisson based Lie 3-algebras within BLG theory, extending previous M5 from M2 results.

Findings

Nambu-Poisson structures enable KK6 from M2 in BLG theory

U(1) field on KK6 can originate from BLG gauge potential

Infinite-dimensional Lie 3-algebras facilitate higher-dimensional brane constructions

Abstract

We study the possibility that the Kaluza-Klein monopole (KK6) world-volume action may be obtained from the multiple membranes (M2) action which is described by BLG theory. We first point out that the infinite dimensional Lie 3-algebra based on the Nambu-Poisson structure could not only provide three dimensional manifolds to allow M5 from M2, which was studied by previous authors, but also provide five dimensional manifolds to allow KK6 from M2. We next present a possible way that the U(1) field on KK6 world-volume action could be produced form the gauge potential in BLG theory.