Light-cone analysis of ungauged and topologically gauged BLG theories

We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons type terms of N=8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.