TY - JOUR
T1 - Fractional quantum Hall effect via holography
T2 - Chern-Simons, edge states and hierarchy
AU - Fujita, Mitsutoshi
AU - Li, Wei
AU - Ryu, Shinsei
AU - Takayanagi, Tadashi
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - 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/Z n.
AB - 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/Z n.
KW - Adscft correspondence
KW - Brane dynamics in gauge theories
KW - Chern-simons theories
KW - Gauge-gravity correspondence
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U2 - 10.1088/1126-6708/2009/06/066
DO - 10.1088/1126-6708/2009/06/066
M3 - Article
AN - SCOPUS:70350020205
VL - 2009
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 6
M1 - 066
ER -