A stringy origin of M2 brane Chern–Simons theories

Abstract

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 Chern–Simons theory dual to AdS 4 × 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 Chern–Simons terms preserve only N = 1 supersymmetry in three dimensions.