Superconformal Chern-Simons theories and AdS 4/CFT 3 correspondence

Abstract

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) × U(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) × U(N)) n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS 4 × S 7/( n × ) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the = 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 × 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. © 2008 SISSA.