2009

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

Fujita, Mitsutoshi, Li, Wei, Ryu, Shinsei et al.

Understand

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.

Built on

E. Witten, “Quantum field theory and the Jones polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
X. G. Wen and A. Zee, “On the Possibility of a Statistics Changing Phase Transition,” J. de Physique 50
1989
Earlier work this paper cites.
S. Elitzur, G. W. Moore, A. Schwimmer and N. Seiberg, “Remarks On The Canonical Quantization Of The Chern-Simons-Witten Theory,” Nucl. Phys. B 326
1989
Earlier work this paper cites.
“The quantum Hall effect, 2nd ed.,” Eds. R. E. Prange and S. M. Girvin, Springer-Verlag, Berlin (1990)
1990
Earlier work this paper cites.
C. G. Callan, J. A. Harvey and A. Strominger, “World sheet approach to heterotic instantons and solitons,” Nucl. Phys. B 359
1991
Earlier work this paper cites.
G. Moore and N. Read, “Nonabelions in the fractional quantum Hall effect,” Nucl. Phys. B 360
1991
Earlier work this paper cites.
V. Periwal, “Topological Closed String Interpretation Of Chern-Simons Theory,” Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
W. Fulton, “Introduction to Toric Varieties,” Princeton University Press (1993)
1993
Earlier work this paper cites.
A. O’Bannon, “Hall Conductivity of Flavor Fields from AdS/CFT,” Phys. Rev. D 76
Original
1994
Earlier work this paper cites.
D. Yoshioka, “The Quantum Hall Effect,” Springer, Solid-State Scineces (1998)
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
E. Witten, “Baryons and branes in anti de Sitter space,” JHEP 9807
1998
Earlier work this paper cites.
O. Aharony and E. Witten, “Anti-de Sitter space and the center of the gauge group,” JHEP 9811
1998
Earlier work this paper cites.
J. Polchinski, “String theory. Vol. 1,2,” Cambridge, UK: Univ. Pr. (1998)
1998
Earlier work this paper cites.
E. Fradkin, Chetan Nayak, A. Tsvelik, and Frank Wilczek, “A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State,” Nucl. Phys. B 516
1998
Earlier work this paper cites.
J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
J. W. Reijnders, F. J. M. van Lankvelt, K. Schoutens, N. Read, “Quantum Hall states and boson triplet condensate for rotating spin-1 bosons,” Phys. Rev. Lett. 89
Original
1999
Earlier work this paper cites.
N. Read and E. Rezyai, “Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level,” Phys. Rev. B 59
1999
Earlier work this paper cites.

Similar

P. Minces and V. O. Rivelles, “Chern-Simons theories in the AdS/CFT correspondence,” Phys. Lett. B 455
1999
Cited alongside, same era.
N. Read and D. Green, “Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect,” Phys. Rev. B 61
2000
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A. P. Polychronakos, “Quantum Hall states as matrix Chern-Simons theory,” JHEP 0104
2001
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2001
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J. M. Maldacena and H. S. Nastase, “The supergravity dual of a theory with dynamical supersymmetry breaking,” JHEP 0109
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2001
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A. Karch and E. Katz, “Adding flavor to AdS/CFT,” JHEP 0206
2002
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X-G. Wen, “Quantum Field Theory of Many-Body Systems,” Oxford University Press (2004)
2004
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T. H. Hansson, Vadim Oganesyan, S. L. Sondhi, “Superconductors are topologically ordered,” Ann. Phys. 313
2004
Cited alongside, same era.

Then

C. L. Kane and E. J. Mele, “ Z 2 Z_{2} Topological Order and the Quantum Spin Hall Effect,” Phys. Rev. Lett. 95
2007
Later among the works it cites.
S. J .Rey, “Quantum Phase Transitions from String Theory,” Talk given at Strings 2007
2007
Later among the works it cites.
S. A. Hartnoll and P. Kovtun, “Hall conductivity from dyonic black holes,” Phys. Rev. D 76
Original
2007
Later among the works it cites.
A. Karch and A. O’Bannon, “Metallic AdS/CFT,” JHEP 0709
Original
2007
Later among the works it cites.
S. Kobayashi, D. Mateos, S. Matsuura, R. C. Myers and R. M. Thomson, “Holographic phase transitions at finite baryon density,” JHEP 0702
2007
Later among the works it cites.
S. G. Naculich and H. J. Schnitzer, “Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory,” JHEP 0706
2007
Later among the works it cites.
T. Nishioka and T. Takayanagi, “AdS bubbles, entropy and closed string tachyons,” JHEP 0701
2007
Later among the works it cites.
P. Fendley, M. P. A. Fisher and C. Nayak, “Topological Entanglement Entropy from the Holographic Partition Function,” J. Statist. Phys. 126
2007
Later among the works it cites.
M. König et al
2008
Later among the works it cites.
E. Keski-Vakkuri and P. Kraus, “Quantum Hall Effect in AdS/CFT,” JHEP 0809
Original
2008
Later among the works it cites.
J. L. Davis, P. Kraus and A. Shah, “Gravity Dual of a Quantum Hall Plateau Transition,” JHEP 0811
Original
2008
Later among the works it cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810
Original
2008
Later among the works it cites.
O. Aharony, O. Bergman and D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
Original
2008
Later among the works it cites.
S. Dong, E. Fradkin, R. G. Leigh and S. Nowling, “Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids,” JHEP 0805
Original
2008
Later among the works it cites.
T. Nishioka and T. Takayanagi, “On Type IIA Penrose Limit and N=6 Chern-Simons Theories,” JHEP 0808
Original
2008
Later among the works it cites.
A. Pakman and A. Parnachev, “Topological Entanglement Entropy and Holography,” JHEP 0807
Original
2008
Later among the works it cites.
I. R. Klebanov, D. Kutasov and A. Murugan, “Entanglement as a Probe of Confinement,” Nucl. Phys. B 796
Original
2008
Later among the works it cites.
T. Nishioka and T. Takayanagi, “Fuzzy Ring from M2-brane Giant Torus,” JHEP 0810
Original
2008
Later among the works it cites.

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