Abstract :
We show that string duality relates M-theory on a local Calabi–Yau fourfold singularity image to type IIA string theory on a Calabi–Yau threefold image 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 image are the well-known quiver theories with image supersymmetry in three dimensions. We show that turning on fluxes, and fibering the image over a direction transverse to the branes, corresponds to turning on image Chern–Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on image in this background become N M2 branes on image. This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi–Yau fourfolds in terms of image quiver Chern–Simons theories. We also provide a new image Chern–Simons theory dual to image. Type IIA/M-theory duality also relates IIA string theory on image with only the RR fluxes turned on, to M-theory on a image holonomy manifold. We show that this implies that the N M2 branes probing the image manifold are described by the quiver Chern–Simons theory originating from the D2 branes probing image, except that now Chern–Simons terms preserve only image supersymmetry in three dimensions.
