NB BLG model in N=8 superfields
  We develop the N=8 superfield description of the Bagger-Lambert-Gustavsson (BLG) model in its Nambu bracket (NB) realization.   The basic ingredient is the octet of scalar d=3 N=8 superfields depending also on the coordinates of a compact three dimensional space M. It is restricted by the 'superembedding-like' equation, which can be treated as covariantization of the linearized superembedding equation for supermembrane (M2-brane) with respect volume preserving diffeomorphisms SDiff3 of M. The curvatures of SDiff3 connection are expressed through the scalar superfields by the N=8 superfield generalization of the Chern-Simons equation (super-CS equation). We show how the dynamical BLG equations appear when studying consistency of these basic equations. 
Igor A. Bandos