Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy
By Mitsutoshi Fujita, Wei Li, S. Ryu, T. Takayanagi. 2009
196 citations recorded by the source corpus.
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 = 6 Chern-Simons theory. We show that D4-branes wrapped on 1 or D8-branes wrapped on 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 2/Zn.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/28f0a06146b734ef01400ad71d4c3ba4a1f2563c
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Citations in the corpus
- Holographic superconductor/insulator transition at zero temperature (2009, methodology): “In the paper [20], this setup has been used to realize the fractional quantum Hall effect by adding D7-branes wrapped on S(5), which is a basic example of topological insulators (see [21] for its back reacted supergravity solution).”
- Holographic entanglement entropy: an overview (2009, background): “In the language of AdS/CFT, we can indeed realize this bulk/edge duality as the AdS3/CFT2 correspondence [73].”
- Holography of dyonic dilaton black branes (2010, background): “Discussions of holography and the quantum Hall system can be found in [12, 37, 38, 39, 40, 41].”
- Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “On the other hand, in [58], the gravity dual of a three dimensional gauge theory which flows in the IR to the pure SU(N) Chern-Simons theory is constructed.”
- Quantum corrections to holographic entanglement entropy (2013, methodology): “In Section 3 of [28] they consider an AdS soliton geometry which is dual to a 3d confining gauge theory.”
- Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “If in addition antiperiodic boundary conditions are imposed for the fermions around the circle, then the theory flows at long distances to a Chern-Simons theory [91].”
- Introduction to holographic superconductor models (2015, methodology): “In addition to holographic superconductors, the holographic approach has been used to understand some other aspects of condensed matter physics, including (non)Fermi liquids [206, 207, 208, 209, 210], quantum Hall effect [211, 212, 213], strange metals [214, 215, 216, 217], topological insulators [2”
- Entanglement entropy from a holographic viewpoint (2012, background): “For studies of holographic entanglement entropy for some other gravity duals including non-conformal theories refer to [91–97].”
- On string theory duals of Lifshitz-like fixed points (2009, methodology): “Our D3-D7 model was originally introduced to model the holographic dual of fractional quantum Hall effects in string theory [22] (refer to [36, 37, 38] for other holographic realizations of quantum Hall effects).”