From Simplified BLG Action to the First-Quantized M-Theory

TL;DR

This paper reviews recent advances in formulating the world-volume action for multiple M2 branes, highlighting a simplified BLG model and proposing a 3D gravity-based approach to M2 brane dynamics.

Contribution

It introduces a simplified BLG action based on Lie algebra without coupling constants and explores a 3D gravity formalism as a potential framework for M2 brane dynamics.

Findings

Simplified BLG action lacks coupling constants and extra fields

Proposes Palatini formalism for 3D supergravity as an M2 brane analogue

Suggests a Polyakov-like formalism for M2 branes

Abstract

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