Lie 3-Algebra and Multiple M2-branes
High Energy Physics - Theory
2009-12-04 v2
Abstract
Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation and the Bagger-Lambert model.
Cite
@article{arxiv.0804.2110,
title = {Lie 3-Algebra and Multiple M2-branes},
author = {Pei-Ming Ho and Ru-Chuen Hou and Yutaka Matsuo},
journal= {arXiv preprint arXiv:0804.2110},
year = {2009}
}
Comments
28 pages