Giant D5 Brane Holographic Hall State

TL;DR

This paper presents a holographic model of quantum Hall states using D5 and D7 branes, revealing integer quantum Hall effects, multiple filling fractions, and potential phase transitions in strongly coupled defect field theories.

Contribution

It introduces a new holographic description of quantum Hall states via D5 and D7 branes, including configurations with multiple filling fractions and symmetry considerations.

Findings

Incompressible charge-gapped state with quantized Hall conductivity at filling fraction one.

Multiple D7 branes correspond to higher filling fractions with residual SU(n) symmetry.

Indications of first-order phase transition related to chiral symmetry restoration.

Abstract

We find a new holographic description of strongly coupled defect field theories using probe D5 branes. We consider a system where a large number of probe branes, which are asymptotically D5 branes, blow up into a D7 brane suspended in the bulk of anti-de Sitter space. For a particular ratio of charge density to external magnetic field, so that the Landau level filling fraction per color is equal to one, the D7 brane exhibits an incompressible charge-gapped state with one unit of integer quantized Hall conductivity. The detailed configuration as well as ungapped, compressible configurations for a range of parameters near the gapped one are found by solving the D5 and D7 brane embedding equations numerically and the D7 is shown to be preferred over the D5 by comparing their energies. We then find integer quantum Hall states with higher filling fractions as a stack of D5 branes which blow up to multiple D7 branes where each D7 brane has filling fraction one. We find indications that the n D7 branes describing the filling fraction n state are coincident with a residual SU(n) symmetry when n is a divisor of the total number of D5 branes. We examine the issue of stability of the larger filling fraction Hall states. We argue that, in the D7 brane phase, chiral symmetry restoration could be a first order phase transition.