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We examine the three-dimensional N = 6 superconformal Chern--Simons theorywith U(N) X U(N) gauge symmetry, which was recently constructed by Aharony,Bergman, Jafferis, and Maldacena (ABJM). Using a formulation with manifestSU(4) R-symmetry and no auxiliary fields, we verify in complete detail both thePoincare supersymmetry and the conformal supersymmetry of the action. Together,these imply the complete OSp(6|4) superconformal symmetry of the theory. Thepotential, which is sixth order in scalar fields, is recast as a sum ofsquares.

Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry