Abstract
We consider three-dimensional maximally superconformal Bagger–Lambert–Gustavsson (BLG) theory and its topologically gauged version (constructed recently in Gran and Nilsson (2009 J. High Energy Phys. JHEP03(2009)074 (arXiv:0809.4478 [hep-th]))) in the light-cone gauge. After eliminating the entire Chern–Simons gauge field, the ungauged BLG light-cone theory looks more conventional and, apart from the order of the interaction terms, resembles super-Yang–Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given at the quadratic order together with a suggested form for the quartic terms. Some problems with constructing the sixth-order interaction terms are also discussed. In the topologically gauged case, we analyze the field equations related to the three Chern–Simons-type terms of conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.
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