ABJM with Flavors and FQHE

TL;DR

The paper extends ABJM theory by incorporating fundamental flavors via D6-branes wrapped on S^3/Z2 in AdS4 x CP3, yielding a holographic dual with N=3 SUSY. It analyzes the D6-brane fluctuations to extract the meson spectrum and operator dimensions, and shows how fractional D2-branes realize a holographic FQHE with external RR fields. The authors also demonstrate a flavor-induced mechanism for fractional QHE plateau transitions, via D6 embedding mass deformations causing changes in the Hall conductance. These results connect brane constructions to condensed matter phenomena in AdS4/CFT3 and suggest directions for finite-temperature conductivities and extended brane setups.

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.