We show that the Baggerâ€“Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal theories in 2 + 1 dimensions. This leads to the Baggerâ€“Lambert theory, with the embedding tensor playing the role of the four-index antisymmetric tensor defining a â€˜3-algebraâ€™. We present an alternative formulation of the theory in which the embedding tensor is replaced by a set of unrestricted scalar fields. By taking these scalar fields to be parity-odd, the Chernâ€“Simons term can be made parity-invariant.
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