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We elaborate on the suggestion made in arXiv:0806.3498 that the 3d \N=8superconformal SU(N) Chern-Simons-matter theory of LorentzianBagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit(involving sending the level k to infinity and redefining the fields) from the\N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman,Jafferis and Maldacena (ABJM). We show that to implement such a limit in aconsistent way one is to extend the ABJM theory by an abelian "ghost"multiplet. The corresponding limit at the 3-algebra level also requiresextending the non-antisymmetric Bagger-Lambert 3-algebra underlying the ABJMtheory by a negative-norm generator. We draw analogy with similar scalinglimits discussed previously for bosonic Chern-Simons theory and comment on someimplications of this relation between the ABJM and L-BLG theories.

On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory