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The manifestly supersymmetric pure spinor formulations of theBagger-Lambert-Gustavsson models with N=8 supersymmetry and theAharony-Bergman-Jafferis-Maldacena models with N=6 supersymmetry are given. Thestructures of the pure spinors are investigated in both cases, andnon-degenerate measures are formed using non-minimal sets of variables,allowing for the formulation of an action principle.

Superfield actions for N=8 and N=6 conformal theories in three dimensions