On relating multiple M2 and D2-branes (original) (raw)

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 fABCDf^{ABC}{}_DfABCD 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 fABCDf^{ABC}{}_DfABCD constructed from the Lie algebra structure constants fabcf^{ab}{}_cfabc of an arbitrary gauge group. Although this choice of fABCDf^{ABC}{}_DfABCD does not admit an obvious Lagrangian description, it does reproduce the correct SYM theory for a stack of NNN D2-branes to leading order in gYM−1g_{YM}^{-1}gYM−1 upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.