A stringy origin of M2 brane Chern-Simons theories

We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X-4 to type IIA string theory on a Calabi-Yau threefold X-3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X-3 are the well-known quiver theories with N = 2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X-3 over a direction transverse to the branes, corresponds to turning on N = 2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X-3 in this background become N M2 branes on X-4. This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N = 2 quiver Chern-Simons theories. We also provide a new N = 2 Chem Simons theory dual to AdS(4) x Q(1,1,1). Type IIA/M-theory duality also relates IIA string theory on X-3 with only the RR fluxes turned on, to M-theory on a G(2) holonomy manifold. We show that this implies that the N M2 branes probing the G(2) manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X-3, except that now Chem Simons terms preserve only N = 1 supersymmetry in three dimensions. (C) 2010 Elsevier B.V. All rights reserved.