Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
arXiv:0901.0924 · doi:10.1088/1126-6708/2009/06/066
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.
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
References in corpus (9)
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
- Entanglement as a Probe of Confinement
- Hall conductivity from dyonic black holes
- Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
- Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
- Transport Properties of Holographic Defects
- Hall Conductivity of Flavor Fields from AdS/CFT
- Classification of abelian spin Chern-Simons theories
Cited by in corpus (7)
- On String Theory Duals of Lifshitz-like Fixed Points
- ABJM with Flavors and FQHE
- Non-Relativistic M2-brane Gauge Theory and New Superconformal Algebra
- Time Reversal Symmetry Breaking Holographic Superconductor in Constant External Magnetic Field
- R^2 Corrections to Asymptotically Lifshitz Spacetimes
- BPS Vortices in Non-relativistic M2-brane Chern-Simons-matter Theory
- Coisotropic D-branes on AdS4 x CP3 and massive deformations