Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy

TL;DR

This paper develops three holographic models from string theory to study fractional quantum Hall effects, including edge states, dualities, and hierarchical structures, providing new insights into topological phases.

Contribution

It introduces novel holographic constructions for FQHE, including edge states, level-rank duality, and hierarchical states, advancing the theoretical understanding of topological quantum matter.

Findings

Holographic edge states reproduce Hall conductivity

Level-rank duality is realized holographically

First string theory embedding of hierarchical FQHE

Abstract

We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on C^2/Z_n.