  We elaborate on the suggestion made in arXiv:0806.3498 that the 3d \N=8
superconformal SU(N) Chern-Simons-matter theory of Lorentzian
Bagger-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 a
consistent way one is to extend the ABJM theory by an abelian "ghost"
multiplet. The corresponding limit at the 3-algebra level also requires
extending the non-antisymmetric Bagger-Lambert 3-algebra underlying the ABJM
theory by a negative-norm generator. We draw analogy with similar scaling
limits discussed previously for bosonic Chern-Simons theory and comment on some
implications of this relation between the ABJM and L-BLG theories.
