8 NB BLG model in N = 8 superfields Igor

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 φ depending also on the coordinates of a compact three dimensional space M3. It is restricted by the superembedding-like equation, DȦφ I = 2iψBγ I BȦ , which can be treated as covariantization of the linearized superembedding equation for supermembrane (M2-brane) with respect volume preserving diffeomorphisms of M3. The curvatures of SDiff3 connection are expressed through φ I by the N=8 superfield generalization of the BLG Chern–Simons equation (super-CS equation). We show how the dynamical BLG equations appear when studying consistency of these basic equations. igor [email protected]; supported by the Basque Science Foundation Ikerbasque.