From simplified BLG action to the first-quantized M theory

Abstract

A concise summary of recent progress in the search for the world-volume action for multiple M2 branes is provided. After the recent discovery of a simplified version of the BLG action, which is based on the ordinary Lie-algebra structure and that does not have coupling constants or extra dynamical fields, attention should be switched to the study of M2 brane dynamics. A viable brane analog of the Polyakov formalism and the Belavin-Knizhnik theorem for strings can probably be provided by the Palatini formalism for a 3d (super-) gravity.