Due to the difficulties of finding superconformal Lagrangian theories for multiple M2-branes, we will in this paper instead focus on the field equations. By relaxing the requirement of a Lagrangian formulation we can explore the possibility of having structure constants $f^{ ABC}{ }_D$ satisfying the fundamental identity but which are not totally antisymmetric. We exemplify this discussion by making use of an explicit choice of a non-antisymmetric $f^{ ABC}{ }_D$ constructed from the Lie algebra structure constants $f^{ ab}{ }_c$ of an arbitrary gauge group. Although this choice of $f^{ ABC}{ }_D$ does not admit an obvious Lagrangian description, it does reproduce the correct SYM theory for a stack of $N$ D2-branes to leading order in $g_{ YM}^{ -1}$ upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.
Categories: hep-th