On relating multiple M2 and D2-branes

Journal article, 2008

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 fABCD 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 fABCD constructed from the Lie algebra structure constants fabc of an arbitrary gauge group. Although this choice of fABCD 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 gYM−1 upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.