李三代數與M膜

Abstract

We review the superconformal Lagrangian describing the low energy dynamics of multiple coinci- dent M2 branes with Lie 3-algebra, and constructed some examples of Lie 3-algebra of ‾nite dimensions. The mathematical structures of Lie 3-algebra encode all the information of the theory. In order to understanding the properties of 11D M theory, and gaining some insight into the degrees of freedom of multiple M2-branes, we also developed the cubic matrix representation. This representation enables us to ‾nd an e®ective ‾eld theory in the large N limit. The fat graph structure and power counting for any Feynman diagram with arbitrary interacting vertices are available. Finally we also got the upper bound of power of N for any diagram with no external legs, but still can not see the N^(3/2) degrees of freedom in M theory.