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

TL;DR

This paper constructs and analyzes N=6 superconformal Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N), exploring their brane origins, dualities, and special cases like the Bagger-Lambert theory, providing evidence for their M2-brane interpretations.

Contribution

It introduces explicit N=6 superconformal theories with brane constructions and dualities, connecting them to M2-branes and string/M-theory backgrounds.

Findings

U(N)xU(N) theory describes N M2-branes on C^4/Z_k

Large N limit dual to M theory on AdS_4xS^7/Z_k

SU(2)xSU(2) case matches Bagger-Lambert theory

Abstract

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. For k=1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d=3 gauge theories. When the gauge group is SU(2)xSU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.