M5 from M2

TL;DR

This work demonstrates that an infinite-dimensional Lie 3-algebra derived from a Nambu-Poisson structure on a 3-manifold, when used in the BLG framework for M2-branes, yields a six-dimensional field theory on M2×N whose bosonic and fermionic content matches that of an M5-brane at low energy. By decomposing fields into modes on N and promoting 3D worldvolume fields to 6D, the authors identify a self-dual 2-form gauge field emerging from the gauge sector, and show the resulting quadratic action reproduces the M5-brane low-energy dynamics. The analysis provides a concrete route to view M5 as a bound state of infinitely many M2s, clarifying the role of Nambu-Poisson 3-algebras and the fundamental identity in M-theory brane relationships, and outlines important open questions about higher-order terms and quantum Nambu structures.

Abstract

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.