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

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arxiv 0901.0924 v3 pith:RXAPWPFB submitted 2009-01-08 hep-th cond-mat.mes-hall

Mitsutoshi Fujita , Wei Li , Shinsei Ryu , Tadashi Takayanagi This is my paper · ORCID
classification hep-thcond-mat.mes-hall
keywords edgehallstatestheorychern-simonsholographicmodelstring
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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.

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Cited by 2 Pith papers

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    A review paper that re-presents earlier results on integrable probe-brane defects and holographic defect correlators without adding a new central result.

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