N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

Understand

We construct three dimensional Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry.

• Using brane constructions we argue that the U(N)xU(N) theory at level k describes the low energy limit of N M2-branes probing a C^4/Z_k singularity.
• At large N the theory is then dual to M theory on AdS_4xS^7/Z_k.
• The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS_4xCP^3.