Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-01-08
JHEP 0906:066,2009
Physics
High Energy Physics
High Energy Physics - Theory
36 pages, 6 figures; v2: with an improved derivation of Hall conductivity in section 3.2, typo corrections, and additional ref
Scientific paper
10.1088/1126-6708/2009/06/066
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.
Fujita Mitsutoshi
Li Wangrong
Ryu Shinsei
Takayanagi Tadashi
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