  We discuss the N=2 superspace formulation of the N=8 superconformal
Bagger-Lambert-Gustavsson theory, and of the N=6 superconformal
Aharony-Bergman-Jafferis-Maldacena U(N)xU(N) Chern-Simons theory. In
particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then
consider orbifold projections of this theory that give non-chiral and chiral
(U(N)xU(N))^n superconformal quiver gauge theories. We argue that these
theories are dual to certain AdS_4 x S^7/(Z_n x Z_k) backgrounds of M-theory.
We also study a SU(3) invariant mass term in the superpotential that makes the
N=8 theory flow to a N=2 superconformal gauge theory with a sextic
superpotential. We conjecture that this gauge theory is dual to the U(1)_R x
SU(3) invariant extremum of the N=8 gauged supergravity, which was discovered
by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more
recently.
