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

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

Mitsutoshi Fujitaa, Wei Lib, Shinsei Ryuc and Tadashi Takayanagib

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[1]
R.E. Prange and S.M. Girvin eds., 1990 The quantum Hall effect, 2nd ed., Springer-Verlag, Berlin Germany

[2]
X-G. Wen, 2004 Quantum field theory of many-body systems, Oxford University Press, Oxford U.K.

[3]
D. Yoshioka, 1998 The quantum Hall effect, Solid-State Sciences, Springer, Germany

[4]
A. Zee, Quantum Hall fluids, [cond-mat/9501022] [http://www-spires.slac.stanford.edu/spires/find/hep/www?irn=3457257]
Preprint 
[5]
E. Witten, 1989 Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 351
CrossRef 
[6]
C.L. Kane and E.J. Mele, 2005 Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95 146802
CrossRef  PubMed 
 
B.A. Bernevig and S.-C. Zhang, 2006 Quantum spin Hall effect, Phys. Rev. Lett. 96 106802
CrossRef  PubMed 
 
R. Roy, On the Z2 classification of quantum spin Hall models, [cond-mat/0604211]
Preprint 
 
J.E. Moore and L. Balents, 2007 Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75 121306(R)
CrossRef 
 
R. Roy, Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect, [cond-mat/0607531]
Preprint 
 
L. Fu, C.L. Kane and E.J. Mele, 2007 Topological insulators in three dimensions, Phys. Rev. Lett. 98 106803
CrossRef  PubMed 
 
A.P. Schnyder, S. Ryu, A. Furusaki and A.W.W. Ludwig, 2008 Classification of topological insulators and superconductors in three spatial dimensions, Phys. Rev. B 78 195125
CrossRef 
 
X.L. Qi, T. Hughes and S.C. Zhang, Topological field theory of time-reversal invariant insulators, [0802.3537]
Preprint  SPIRES 
[7]
M. König et al., 2007 Quantum spin Hall insulator state in HgTe quantum wells, Science 318 766
CrossRef  PubMed 
 
D. Hsieh et al., 2008 Topological phases of time-reversal invariant superconductors and electronic systems with sublattice (chiral) symmetry, in three spatial dimensions, Nature 452 970
CrossRef  PubMed 
[8]
J.M. Maldacena, 1998 The large-N limit of superconformal field theories and supergravity Adv. Theor. Math. Phys. 2 231 [hep-th/9711200]
Preprint  SPIRES 
 
J.M. Maldacena, 1999 Int. J. Theor. Phys. 38 1113
CrossRef 
[9]
L. Susskind, The quantum Hall fluid and non-commutative Chern Simons theory, [hep-th/0101029]
Preprint  SPIRES 
[10]
A.P. Polychronakos, 2001 Quantum Hall states as matrix Chern-Simons theory J. High Energy Phys. JHEP04(2001)011 [hep-th/0103013]
IOPscience  Preprint  SPIRES 
 
A.P. Polychronakos, 2001 Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory J. High Energy Phys. JHEP06(2001)070 [hep-th/0106011]
IOPscience  Preprint  SPIRES 
[11]
S. Hellerman and M. Van Raamsdonk, 2001 Quantum Hall physics equals noncommutative field theory J. High Energy Phys. JHEP10(2001)039 [hep-th/0103179]
IOPscience  Preprint  SPIRES 
[12]
S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, [hep-th/0107200]
Preprint  SPIRES 
[13]
J.H. Brodie, 2001 D-branes in massive IIA and solitons in Chern-Simons theory J. High Energy Phys. JHEP11(2001)014 [hep-th/0012068]
IOPscience  Preprint  SPIRES 
[14]
J.H. Brodie, L. Susskind and N. Toumbas, 2001 How Bob Laughlin tamed the giant graviton from Taub-NUT space J. High Energy Phys. JHEP02(2001)003 [hep-th/0010105]
IOPscience  Preprint  SPIRES 
[15]
O. Bergman, Y. Okawa and J.H. Brodie, 2001 The stringy quantum Hall fluid J. High Energy Phys. JHEP11(2001)019 [hep-th/0107178]
IOPscience  Preprint  SPIRES 
[16]
E. Keski-Vakkuri and P. Kraus, 2008 Quantum Hall effect in AdS/CFT J. High Energy Phys. JHEP09(2008)130 [0805.4643]
IOPscience  Preprint  SPIRES 
[17]
J.L. Davis, P. Kraus and A. Shah, 2008 Gravity dual of a quantum Hall plateau transition J. High Energy Phys. JHEP11(2008)020 [0809.1876]
IOPscience  Preprint  SPIRES 
[18]
S.J. Rey, Quantum phase transitions from string theory, talk given at Strings 2007, Madrid Spain

[19]
S.A. Hartnoll and P. Kovtun, 2007 Hall conductivity from dyonic black holes, Phys. Rev. D 76 066001 [0704.1160]
CrossRef  Preprint  SPIRES 
[20]
A. O'Bannon, 2007 Hall conductivity of flavor fields from AdS/CFT, Phys. Rev. D 76 086007 [0708.1994]
CrossRef  Preprint  SPIRES 
[21]
R.C. Myers and M.C. Wapler, 2008 Transport properties of holographic defects J. High Energy Phys. JHEP12(2008)115 [0811.0480]
IOPscience  Preprint  SPIRES 
[22]
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, 2008 N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals J. High Energy Phys. JHEP10(2008)091 [0806.1218]
IOPscience  Preprint  SPIRES 
[23]
O. Aharony, O. Bergman and D.L. Jafferis, 2008 Fractional M2-branes J. High Energy Phys. JHEP11(2008)043 [0807.4924]
IOPscience  Preprint  SPIRES 
[24]
E. Witten, 1998 Anti-de Sitter space, thermal phase transition and confinement in gauge theories Adv. Theor. Math. Phys. 2 505 [hep-th/9803131]
Preprint  SPIRES 
[25]
A. Kitaev and J. Preskill, 2006 Topological entanglement entropy, Phys. Rev. Lett. 96 110404 [hep-th/0510092]
CrossRef  Preprint  PubMed  SPIRES 
[26]
M. Levin and X-G. Wen, 2006 Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96 110405 [cond-mat/0510613]
CrossRef  Preprint  PubMed 
[27]
S. Dong, E. Fradkin, R.G. Leigh and S. Nowling, 2008 Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids J. High Energy Phys. JHEP05(2008)016 [0802.3231]
IOPscience  Preprint  SPIRES 
[28]
T. Nishioka and T. Takayanagi, 2008 On type IIA Penrose limit and N=6 Chern-Simons theories J. High Energy Phys. JHEP08(2008)001 [0806.3391]
IOPscience  Preprint  SPIRES 
[29]
F.E. Camino et al., 2005 Aharonov-Bohm superperiod in a Laughlin quasiparticle interferometer, Phys. Rev. Lett. 95 246802
CrossRef  PubMed 
 
F.E. Camino et al., 2005 Realization of a Laughlin quasiparticle interferometer: observation of fractional statistics, Phys. Rev. B 72 075342
CrossRef 
 
E.-A. Kim, 2006 Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer, Phys. Rev. Lett. 97 216404
CrossRef  PubMed 
 
B. Rosenow and B.I. Halperin, 2007 Influence of interactions on flux and back-gate period of quantum Hall interferometers, Phys. Rev. Lett. 98 106801
CrossRef  PubMed 
 
J.K. Jain and C. Shi, 2006 Resonant tunneling in the fractional quantum Hall effect: superperiods and braiding statistics, Phys. Rev. Lett. 96 136802
CrossRef  PubMed 
 
M. Grayson et al., 2007 Novel metallic and insulating states at a bent quantum Hall junction, Phys. Rev. B 76 201304(R)
CrossRef 
[30]
X.G. Wen and A. Zee, 1989 On the possibility of a statistics changing phase transition, J. Phys. (France) 50 1623 [NSF-ITP-88-114]
CrossRef 
[31]
A. Karch and A. O'Bannon, 2007 Metallic AdS/CFT J. High Energy Phys. JHEP09(2007)024 [0705.3870]
IOPscience  Preprint  SPIRES 
[32]
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, 2007 Holographic phase transitions at finite baryon density J. High Energy Phys. JHEP02(2007)016 [hep-th/0611099]
IOPscience  Preprint  SPIRES 
[33]
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, 1989 Remarks on the canonical quantization of the Chern-Simons-Witten theory, Nucl. Phys. B 326 108
CrossRef 
[34]
J.M. Maldacena and H.S. Nastase, 2001 The supergravity dual of a theory with dynamical supersymmetry breaking J. High Energy Phys. JHEP09(2001)024 [hep-th/0105049]
IOPscience  Preprint  SPIRES 
[35]
S.G. Naculich and H.J. Schnitzer, 2007 Level-rank duality of the U(N) WZW model, Chern-Simons theory and 2 D qYM theory J. High Energy Phys. JHEP06(2007)023 [hep-th/0703089]
IOPscience  Preprint  SPIRES 
[36]
E. Witten, 1998 Baryons and branes in anti de Sitter space J. High Energy Phys. JHEP07(1998)006 [hep-th/9805112]
IOPscience  Preprint  SPIRES 
[37]
A. Karch and E. Katz, 2002 Adding flavor to AdS/CFT J. High Energy Phys. JHEP06(2002)043 [hep-th/0205236]
IOPscience  Preprint  SPIRES 
[38]
O. Aharony and E. Witten, 1998 Anti-de Sitter space and the center of the gauge group J. High Energy Phys. JHEP11(1998)018 [hep-th/9807205]
IOPscience  Preprint  SPIRES 
[39]
A. Pakman and A. Parnachev, 2008 Topological entanglement entropy and holography J. High Energy Phys. JHEP07(2008)097 [0805.1891]
IOPscience  Preprint  SPIRES 
[40]
S. Ryu and T. Takayanagi, 2006 Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 181602 [hep-th/0603001]
CrossRef  Preprint  PubMed  SPIRES 
 
S. Ryu and T. Takayanagi, 2006 Aspects of holographic entanglement entropy J. High Energy Phys. JHEP08(2006)045 [hep-th/0605073]
IOPscience  Preprint  SPIRES 
[41]
D.V. Fursaev, 2006 Proof of the holographic formula for entanglement entropy J. High Energy Phys. JHEP09(2006)018 [hep-th/0606184]
IOPscience  Preprint  SPIRES 
[42]
T. Nishioka and T. Takayanagi, 2007 AdS bubbles, entropy and closed string tachyons J. High Energy Phys. JHEP01(2007)090 [hep-th/0611035]
IOPscience  Preprint  SPIRES 
[43]
I.R. Klebanov, D. Kutasov and A. Murugan, 2008 Entanglement as a probe of confinement, Nucl. Phys. B 796 274 [0709.2140]
CrossRef  Preprint  SPIRES 
[44]
V. Periwal, 1993 Topological closed string interpretation of Chern-Simons theory, Phys. Rev. Lett. 71 1295 [hep-th/9305115]
CrossRef  Preprint  PubMed  SPIRES 
[45]
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, Chern-Simons gauge theory and the AdS3/CFT2 correspondence, [hep-th/0403225]
Preprint  SPIRES 
 
D. Belov and G.W. Moore, Classification of abelian spin Chern-Simons theories, [hep-th/0505235]
Preprint  SPIRES 
[46]
J. Polchinski, 1998 String theory, vol. 1 and 2, Cambridge University Press, Cambridge U.K.
CrossRef 
[47]
C.G. Callan Jr., J.A. Harvey and A. Strominger, 1991 World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 611
CrossRef 
[48]
A. Adams, J. Polchinski and E. Silverstein, 2001 Don't panic! Closed string tachyons in ALE space-times J. High Energy Phys. JHEP10(2001)029 [hep-th/0108075]
IOPscience  Preprint  SPIRES 
[49]
J.A. Harvey, D. Kutasov, E.J. Martinec and G.W. Moore, Localized tachyons and RG flows, [hep-th/0111154]
Preprint  SPIRES 
[50]
W. Fulton, 1993 Introduction to toric varieties, Princeton University Press, Princeton U.S.A.

[51]
G.W. Moore and A. Parnachev, 2004 Localized tachyons and the quantum McKay correspondence J. High Energy Phys. JHEP11(2004)086 [hep-th/0403016]
IOPscience  Preprint  SPIRES 
 
G.W. Moore and A. Parnachev, 2006 Profiling the brane drain in a nonsupersymmetric orbifold J. High Energy Phys. JHEP01(2006)024 [hep-th/0507190]
IOPscience  Preprint  SPIRES 
[52]
P. Fendley, M.P.A. Fisher and C. Nayak, 2007 Topological entanglement entropy from the holographic partition function, J. Stat. Phys. 126 1111 [cond-mat/0609072]
CrossRef  Preprint  SPIRES 
[53]
J.W. Reijnders, F.J.M. van Lankvelt, K. Schoutens and N. Read, 2002 Quantum Hall states and boson triplet condensate for rotating spin-1 bosons, Phys. Rev. Lett. 89 120401
CrossRef  PubMed 
 
N.R. Cooper, N.K. Wilkin and J.M.F. Gunn, 2001 Quantum phases of vortices in rotating Bose-Einstein condensates, Phys. Rev. Lett. 87 120405
CrossRef  PubMed 
 
N.R. Cooper and N.K. Wilkin, 1999 A composite fermion description of rotating Bose-Einstein condensates, Phys. Rev. B 60 R16279
CrossRef 
 
N.K. Wilkin and J.M.F. Gunn, Condensation of `composite bosons' in a rotating BEC, [cond-mat/9906282]
Preprint 
 
N.R. Cooper, Rapidly rotating atomic gases, [0810.4398]
Preprint 
[54]
G.W. Moore and N. Read, 1991 NonAbelians in the fractional quantum Hall effect, Nucl. Phys. B 360 362
CrossRef 
[55]
E.H. Fradkin, C. Nayak, A. Tsvelik and F. Wilczek, 1998 A Chern-Simons effective field theory for the Pfaffian quantum Hall state, Nucl. Phys. B 516 704 [cond-mat/9711087]
CrossRef  Preprint  SPIRES 
[56]
N. Read and D. Green, 2000 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 10267 [cond-mat/9906453]
CrossRef  Preprint  SPIRES 
[57]
N. Read and E. Rezayi, 1999 Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level, Phys. Rev. B 59 8084 [cond-mat/9809384]
CrossRef  Preprint  SPIRES 
[58]
T.H. Hansson, V. Oganesyan and S.L. Sondhi, 2004 Superconductors are topologically ordered, Ann. Phys. (NY) 313 497
CrossRef 
[59]
S.-P. Kou, M. Levin and X.-G. Wen, Mutual Chern-Simons theory for Z2 topological order, [0803.2300]
Preprint  SPIRES 
[60]
C. Xu and S. Sachdev, Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory, [0811.1220]
Preprint  SPIRES 
[61]
D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, [0901.0969]
Preprint  SPIRES 
[62]
T. Nishioka and T. Takayanagi, 2008 Fuzzy ring from M2-brane giant torus J. High Energy Phys. JHEP10(2008)082 [0808.2691]
IOPscience  Preprint  SPIRES 
[63]
P. Minces and V.O. Rivelles, 1999 Chern-Simons theories in the AdS/CFT correspondence, Phys. Lett. B 455 147 [hep-th/9902123]
CrossRef  Preprint  SPIRES 
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