Gauge symmetry and supersymmetry of multiple M2-branes

In previous work we proposed a field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product. In this paper we gauge a symmetry that arises from the algebra's triple product. We then construct a supersymmetric theory that is consistent with all the symmetries expected of a multiple M2-brane theory: 16 supersymmetries, conformal invariance, and an $SO(8)$ R-symmetry that acts on the eight transverse scalars. The gauge field is not dynamical. The result is a new type of maximally supersymmetric gauge theory in three dimensions.