Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy

2009/01/31 by Mitsutoshi Fujita, Wei Li, Shinsei Ryu +1 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Brane cosmology #Chern–Simons theory #Electron #Fractional quantum Hall effect #Gauge theory #Mathematical physics #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Quantum spin Hall effect #String theory #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1088/1126-6708/2009/06/066

published as JHEP 0906:066,2009 · 36 pages, 6 figures; v2: with an improved derivation of Hall conductivity in section 3.2, typo corrections, and additional references; v3: explanations and comments added

arxiv created 2009/04/21 · openalex publication_date 2009/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 CP¹ or D8-branes wrapped on CP³ 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 C²/Z_n.

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