Abstract
We find a new holographic description of strongly coupled defect field theories using probe D5 branes. We consider a system where a large number of probe branes, which are asymptotically D5 branes, blow up into a D7 brane suspended in the bulk of anti-de Sitter space. For a particular ratio of charge density to external magnetic field, so that the Landau level filling fraction per color is equal to one, the D7 brane exhibits an incompressible charge-gapped state with one unit of integer quantized Hall conductivity. The detailed configuration as well as ungapped, compressible configurations for a range of parameters near the gapped one are found by solving the D5 and D7 brane embedding equations numerically and the D7 is shown to be preferred over the D5 by comparing their energies. We then find integer quantum Hall states with higher filling fractions as a stack of D5 branes which blow up to multiple D7 branes where each D7 brane has filling fraction one. We find indications that the ν D7 branes describing the filling fraction ν state are coincident with a residual SU(ν) symmetry when ν is a divisor of the total number of D5 branes. We examine the issue of stability of the larger filling fraction Hall states. We argue that, in the D7 brane phase, chiral symmetry restoration could be a first order phase transition.
Similar content being viewed by others
References
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
S. Sethi, The matrix formulation of type IIB five-branes, Nucl. Phys. B 523 (1998) 158 [hep-th/9710005] [INSPIRE].
A. Kapustin and S. Sethi, The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 (1998) 571 [hep-th/9804027] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
J. Erdmenger, Z. Guralnik and I. Kirsch, Four-dimensional superconformal theories with interacting boundaries or defects, Phys. Rev. D 66 (2002) 025020 [hep-th/0203020] [INSPIRE].
V.G. Filev, C.V. Johnson and J.P. Shock, Universal holographic chiral dynamics in an external magnetic field, JHEP 08 (2009) 013 [arXiv:0903.5345] [INSPIRE].
R.C. Myers and M.C. Wapler, Transport properties of holographic defects, JHEP 12 (2008) 115 [arXiv:0811.0480] [INSPIRE].
N. Evans and E. Threlfall, Chemical potential in the gravity dual of a 2+1 dimensional system, Phys. Rev. D 79 (2009) 066008 [arXiv:0812.3273] [INSPIRE].
V.G. Filev, Hot defect superconformal field theory in an external magnetic field, JHEP 11 (2009) 123 [arXiv:0910.0554] [INSPIRE].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Holographic description of the phase diagram of a chiral symmetry breaking gauge theory, JHEP 03 (2010) 132 [arXiv:1002.1885] [INSPIRE].
K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett. B 698 (2011) 91 [arXiv:1003.2694] [INSPIRE].
S.S. Pal, Quantum phase transition in a Dp-Dq system, Phys. Rev. D 82 (2010) 086013 [arXiv:1006.2444] [INSPIRE].
N. Evans, K. Jensen and K.-Y. Kim, Non mean-field quantum critical points from holography, Phys. Rev. D 82 (2010) 105012 [arXiv:1008.1889] [INSPIRE].
G. Grignani, N. Kim and G.W. Semenoff, D3-D5 holography with flux, Phys. Lett. B 715 (2012) 225 [arXiv:1203.6162] [INSPIRE].
G. Grignani, N. Kim and G.W. Semenoff, D7-anti-D7 bilayer: holographic dynamical symmetry breaking, Phys. Lett. B 722 (2013) 360 [arXiv:1208.0867] [INSPIRE].
K. Nagasaki and S. Yamaguchi, Expectation values of chiral primary operators in holographic interface CFT, Phys. Rev. D 86 (2012) 086004 [arXiv:1205.1674] [INSPIRE].
C. Kristjansen, G.W. Semenoff and D. Young, Chiral primary one-point functions in the D3-D7 defect conformal field theory, JHEP 01 (2013) 117 [arXiv:1210.7015] [INSPIRE].
D.K. Brattan, R.A. Davison, S.A. Gentle and A. O’Bannon, Collective excitations of holographic quantum liquids in a magnetic field, JHEP 11 (2012) 084 [arXiv:1209.0009] [INSPIRE].
K.G. Klimenko, Three-dimensional Gross-Neveu model in an external magnetic field, Theor. Math. Phys. 89 (1992) 1161 [INSPIRE].
V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. Lett. 73 (1994) 3499 [Erratum ibid. 76 (1996) 1005] [hep-ph/9405262] [INSPIRE].
V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. D 52 (1995) 4718 [hep-th/9407168] [INSPIRE].
G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, Phase transition induced by a magnetic field, Mod. Phys. Lett. A 13 (1998) 1143 [hep-ph/9803371] [INSPIRE].
G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, Universality and the magnetic catalysis of chiral symmetry breaking, Phys. Rev. D 60 (1999) 105024 [hep-th/9905116] [INSPIRE].
G.W. Semenoff and F. Zhou, Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene, JHEP 07 (2011) 037 [arXiv:1104.4714] [INSPIRE].
S. Bolognesi and D. Tong, Magnetic catalysis in AdS 4, Class. Quant. Grav. 29 (2012) 194003 [arXiv:1110.5902] [INSPIRE].
J. Erdmenger, V.G. Filev and D. Zoakos, Magnetic catalysis with massive dynamical flavours, JHEP 08 (2012) 004 [arXiv:1112.4807] [INSPIRE].
S. Bolognesi, J.N. Laia, D. Tong and K. Wong, A gapless hard wall: magnetic catalysis in bulk and boundary, JHEP 07 (2012) 162 [arXiv:1204.6029] [INSPIRE].
I.A. Shovkovy, Magnetic catalysis: a review, Lect. Notes Phys. 871 (2013) 13 [arXiv:1207.5081] [INSPIRE].
M. Blake, S. Bolognesi, D. Tong and K. Wong, Holographic dual of the lowest Landau level, JHEP 12 (2012) 039 [arXiv:1208.5771] [INSPIRE].
V.G. Filev and M. Ihl, Flavoured large-N gauge theory on a compact space with an external magnetic field, JHEP 01 (2013) 130 [arXiv:1211.1164] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
C.G. Callan and J.M. Maldacena, Brane death and dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198 [hep-th/9708147] [INSPIRE].
H.A. Fertig, Energy spectrum of a layered system in a strong magnetic field, Phys. Rev. B 40 (1989) 1087.
T. Jungwirth and A.H. MacDonald, Pseudospin anisotropy classification of quantum Hall ferromagnets, Phys. Rev. B 63 (2001) 035305 [cond-mat/0003430].
Z.F. Ezawa and K. Hasebe, Interlayer exchange interactions, SU(4) soft waves and skyrmions in bilayer quantum Hall ferromagnets, Phys. Rev. B 65 (2002) 075311 [cond-mat/0104448] [INSPIRE].
S.Q. Murphy, J.P. Eisenstein, G.S. Boebinger, L.W. Pfeiffer and K.W. West, Many-body integer quantum Hall effect: evidence for new phase transitions, Phys. Rev. Lett. 72 (1994) 728.
S.R. Coleman and B.R. Hill, No more corrections to the topological mass term in QED in three-dimensions, Phys. Lett. B 159 (1985) 184 [INSPIRE].
G.W. Semenoff, P. Sodano and Y.-S. Wu, Renormalization of the statistics parameter in three-dimensional electrodynamics, Phys. Rev. Lett. 62 (1989) 715 [INSPIRE].
J.D. Lykken, J. Sonnenschein and N. Weiss, The theory of anyonic superconductivity: a review, Int. J. Mod. Phys. A 6 (1991) 5155 [INSPIRE].
A.J. Niemi and G.W. Semenoff, Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett. 51 (1983) 2077 [INSPIRE].
A.N. Redlich, Gauge noninvariance and parity violation of three-dimensional fermions, Phys. Rev. Lett. 52 (1984) 18 [INSPIRE].
O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall effect in a holographic model, JHEP 10 (2010) 063 [arXiv:1003.4965] [INSPIRE].
N. Jokela, G. Lifschytz and M. Lippert, Magneto-roton excitation in a holographic quantum Hall fluid, JHEP 02 (2011) 104 [arXiv:1012.1230] [INSPIRE].
N. Jokela, M. Jarvinen and M. Lippert, A holographic quantum Hall model at integer filling, JHEP 05 (2011) 101 [arXiv:1101.3329] [INSPIRE].
O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].
N. Jokela, M. Jarvinen and M. Lippert, Fluctuations of a holographic quantum Hall fluid, JHEP 01 (2012) 072 [arXiv:1107.3836] [INSPIRE].
N. Jokela, G. Lifschytz and M. Lippert, Magnetic effects in a holographic Fermi-like liquid, JHEP 05 (2012) 105 [arXiv:1204.3914] [INSPIRE].
J.L. Davis, P. Kraus and A. Shah, Gravity dual of a quantum Hall plateau transition, JHEP 11 (2008) 020 [arXiv:0809.1876] [INSPIRE].
S.-J. Rey, String theory on thin semiconductors: holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [INSPIRE].
D. Kutasov, J. Lin and A. Parnachev, Conformal phase transitions at weak and strong coupling, Nucl. Phys. B 858 (2012) 155 [arXiv:1107.2324] [INSPIRE].
J.L. Davis, H. Omid and G.W. Semenoff, Holographic fermionic fixed points in D = 3, JHEP 09 (2011) 124 [arXiv:1107.4397] [INSPIRE].
J.L. Davis and N. Kim, Flavor-symmetry breaking with charged probes, JHEP 06 (2012) 064 [arXiv:1109.4952] [INSPIRE].
H. Omid and G.W. Semenoff, D3-D7 holographic dual of a perturbed 3D CFT, arXiv:1208.5176 [INSPIRE].
M. Goykhman, A. Parnachev and J. Zaanen, Fluctuations in finite density holographic quantum liquids, JHEP 10 (2012) 045 [arXiv:1204.6232] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1212.5609
Rights and permissions
About this article
Cite this article
Kristjansen, C., Semenoff, G.W. Giant D5 brane holographic Hall state. J. High Energ. Phys. 2013, 48 (2013). https://doi.org/10.1007/JHEP06(2013)048
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2013)048