ABJM with Flavors and FQHE

Abstract

We add fundamental matters to the N=6 Chern-Simons theory (ABJM theory), and show that D6-branes wrapped over AdS_4 x S^3/Z_2 in type IIA superstring theory on AdS_4 x CP^3 give its dual description with N=3 supersymmetry. We confirm this by the arguments based on R-symmetry, supersymmetry, and brane configuration of ABJM theory. We also analyze the fluctuations of the D6-brane and compute the conformal dimensions of dual operators. In the presence of fractional branes, the ABJM theory can model the fractional quantum Hall effect (FQHE), with RR-fields regarded as the external electric-magnetic field. We show that an addition of the flavor D6-brane describes a class of fractional quantum Hall plateau transition.