Script N = 6 superconformal ChernSimonsmatter theories, M2branes and their gravity duals
Abstract
We construct three dimensional ChernSimonsmatter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit Script N = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2branes probing a C^{4}/Z_{k} singularity. At large N the theory is then dual to Mtheory on AdS_{4} × S^{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_{4} × CP^{3}. For k = 1 the theory is conjectured to describe N M2branes 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) × SU(2) our theory has extra symmetries and becomes identical to the BaggerLambert theory.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2008
 DOI:
 10.1088/11266708/2008/10/091
 arXiv:
 arXiv:0806.1218
 Bibcode:
 2008JHEP...10..091A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 41 pages, 4 figures. v3: minor corrections, added references. v4: added reference, minor changes, JHEP version