Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-10
JHEP 0810:067,2008
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, references added and statements concerning the fundamental identity revised
Scientific paper
10.1088/1126-6708/2008/10/067
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.
Gran Ulf
Nilsson Bengt E. W.
Petersson Christoffer
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