Abstract: The manifestly supersymmetric pure spinor formulations of the Bagger– Lambert–Gustavsson models with N = 8 supersymmetry and the Aharony–Bergman–Jafferis–Maldacena models with N = 6 supersymmetry are given. The structures of the pure spinors are investigated in both cases, and non-degenerate measures are formed using non-minimal sets of variables, allowing for the formulation of an action principle. 2................................ M. Cederwall: “Superfield actions for N=8 and N=6...” There has recently been much interest in conformal three-dimensional theories. Following the discovery of the existence of a maximally supersymmetric (N = 8) interacting theory of scalar multiplets coupled to Chern–Simons, the Bagger–Lambert–Gustavsson (BLG) theory [1,2,3,4], much effort has been spent on trying to generalise the construction and to interpret it in terms of an AdS boundary model of multiple M2-branes. The interesting, but restrictive, algebraic structure of the model, containing a 3-algebra with antisymmetric structure constants, turned out to have only one finite-dimensional realisation [5,6], possible to interpret in term of two M2-branes [7,8] (see however refs. [9,10] dealing with the infinite-dimensional solution related to volume-preserving diffeomorphisms in three dimensions)
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