ABJM with Flavors and FQHE

TL;DR

This paper extends the ABJM theory by adding flavors via D6-branes, explores its supersymmetric dual description, and models fractional quantum Hall effects through brane configurations and fluctuations.

Contribution

It introduces fundamental matter into ABJM theory using D6-branes, confirming the duality and analyzing FQHE phenomena within this framework.

Findings

D6-branes wrapped on AdS_4 x S^3/Z_2 preserve N=3 supersymmetry.

Fluctuation analysis yields conformal dimensions of dual operators.

Flavor D6-branes model fractional quantum Hall plateau transitions.

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.