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

Mitsutoshi Fujita et al JHEP06(2009)066   doi: 10.1088/1126-6708/2009/06/066  Help

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Mitsutoshi Fujitaa, Wei Lib, Shinsei Ryuc and Tadashi Takayanagib
a Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan
b Institute for Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwa, Chiba 277-8582, Japan
c Department of Physics, University of California, 366 LeConte Hall MC 7300, Berkeley, CA 94720-7300, U.S.A.
E-mail: mfujita@gauge.scphys.kyoto-u.ac.jp, wei.li@ipmu.jp, sryu@berkeley.edu and tadashi.takayanagi@ipmu.jp

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 Script N = 6 Chern-Simons theory. We show that D4-branes wrapped on Bbb CBbb P1 or D8-branes wrapped on Bbb CBbb P3 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 Bbb C2/Zn.

Key words: Chern-Simons Theories; AdS-CFT Correspondence; Brane Dynamics in Gauge Theories; Gauge-gravity correspondence

E-print number: 0901.0924
Cited: by
Refers: to

Received 26 February 2009, accepted for publication 31 May 2009
Published 22 June 2009

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