Abstract
We study parity-violating effects, particularly the generation of angular momentum density and its relation to the parity-odd and dissipationless transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems in 2+1 dimensions using holographic method. We employ a class of 3+1-dimensional holographic models of Einstein-Maxwell system with gauge and gravitational Chern-Simons terms coupled to a dynamical scalar field. The scalar can condensate and break the parity spontaneously. We find that when the scalar condensates, a non-vanishing angular momentum density and an associated edge current are generated, and they receive contributions from both gauge and gravitational Chern-Simons terms. The angular momentum density does not satisfy a membrane paradigm form because the vector mode fluctuations from which it is calculated are effectively massive. On the other hand, the emergence of Hall viscosity is a consequence of the gravitational Chern-Simons term alone and it has membrane paradigm form. We present both general analytic results and numeric results which take back-reactions into account. The ratio between Hall viscosity and angular momentum density resulting from the gravitational Chern-Simons term has in general a deviation from the universal 1/2 value obtained from field theory and condensed matter physics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz et al., Parity-Violating Hydrodynamics in 2+1 Dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
M. Kaminski and S. Moroz, Non-Relativistic Parity-Violating Hydrodynamics in Two Spatial Dimensions, Phys. Rev. B 89 (2014) 115418 [arXiv:1310.8305] [INSPIRE].
J.E. Avron, R. Seiler and P.G. Zograf, Viscosity of quantum Hall fluids, Phys. Rev. Lett. 75 (1995) 697 [INSPIRE].
J.E. Avron, Odd Viscosity, J. Stat. Phys. 92 (1998) 543 [physics/9712050].
I.V. Tokatly and G. Vignale, Lorentz shear modulus of a two-dimensional electron gas at high magnetic field, Phys. Rev. B 76 (2007) 161305 [arXiv:0706.2454].
I.V. Tokatly and G. Vignale, Lorentz shear modulus of fractional quantum Hall states, J. Phys. Cond. Matt. 21 (2009) A275603 [arXiv:0812.4331].
N. Read, Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p(x) + ip(y) paired superfluids, Phys. Rev. B 79 (2009) 045308 [arXiv:0805.2507] [INSPIRE].
F.D.M. Haldane, ’Hall viscosity’ and intrinsic metric of incompressible fractional Hall fluids, arXiv:0906.1854 [INSPIRE].
N. Read and E.H. Rezayi, Hall viscosity, orbital spin and geometry: paired superfluids and quantum Hall systems, Phys. Rev. B 84 (2011) 085316 [arXiv:1008.0210] [INSPIRE].
T.L. Hughes, R.G. Leigh and E. Fradkin, Torsional Response and Dissipationless Viscosity in Topological Insulators, Phys. Rev. Lett. 107 (2011) 075502 [arXiv:1101.3541] [INSPIRE].
T.L. Hughes, R.G. Leigh and O. Parrikar, Torsional Anomalies, Hall Viscosity and Bulk-boundary Correspondence in Topological States, Phys. Rev. D 88 (2013) 025040 [arXiv:1211.6442] [INSPIRE].
B. Bradlyn, M. Goldstein and N. Read, Kubo formulas for viscosity: Hall viscosity, Ward identities and the relation with conductivity, Phys. Rev. B 86 (2012) 245309 [arXiv:1207.7021] [INSPIRE].
C. Hoyos and D.T. Son, Hall Viscosity and Electromagnetic Response, Phys. Rev. Lett. 108 (2012) 066805 [arXiv:1109.2651] [INSPIRE].
A. Nicolis and D.T. Son, Hall viscosity from effective field theory, arXiv:1103.2137 [INSPIRE].
C. Hoyos, S. Moroz and D.T. Son, Effective theory of chiral two-dimensional superfluids, Phys. Rev. B 89 (2014) 174507 [arXiv:1305.3925] [INSPIRE].
D.T. Son, Newton-Cartan Geometry and the Quantum Hall Effect, arXiv:1306.0638 [INSPIRE].
Y. Hidaka, Y. Hirono, T. Kimura and Y. Minami, Viscoelastic-electromagnetism and Hall viscosity, PTEP 2013 (2013) 013A02 [arXiv:1206.0734] [INSPIRE].
P.B. Wiegmann, Quantum Hydrodynamics of Fractional Hall Effect: Quantum Kirchhoff Equations, arXiv:1211.5132.
P.B. Wiegmann, Anomalous Hydrodynamics of Fractional Quantum Hall States, J. Exp. Theor. PHYS. 144 (9) (2013) 617 Soviet Journal of Experimental and Theoretical Physics 117 (2013) 538 [arXiv:1305.6893].
P.B. Wiegmann, Hydrodynamics of Euler incompressible fluid and the Fractional Quantum Hall Effect, Phys. Rev. B 88 (2013) 241305 [arXiv:1309.5992].
M. Stone and R. Roy, Edge modes, edge currents, and gauge invariance in superfluids and superconductors, Phys. Rev. B 69 (2004) 184511 [cond-mat/0308034].
J.A. Sauls, Surface States, Edge Currents and the Angular Momentum of Chiral-wave Superfluids, Phys. Rev. B 84 (2011) 214509 [arXiv:1209.5501].
Y. Tsutsumi and K. Machida, Edge mass current and the role of Majorana fermions in a-phase superfluid He-3, Phys. Rev. B 85 (2012) 100506 [arXiv:1110.5409] [INSPIRE].
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Saremi and D.T. Son, Hall viscosity from gauge/gravity duality, JHEP 04 (2012) 091 [arXiv:1103.4851] [INSPIRE].
J.-W. Chen, N.-E. Lee, D. Maity and W.-Y. Wen, A Holographic Model For Hall Viscosity, Phys. Lett. B 713 (2012) 47 [arXiv:1110.0793] [INSPIRE].
J.-W. Chen, S.-H. Dai, N.-E. Lee and D. Maity, Novel Parity Violating Transport Coefficients in 2+1 Dimensions from Holography, JHEP 09 (2012) 096 [arXiv:1206.0850] [INSPIRE].
R.-G. Cai, T.-J. Li, Y.-H. Qi and Y.-L. Zhang, Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term, Phys. Rev. D 86 (2012) 086008 [arXiv:1208.0658] [INSPIRE].
D.-C. Zou and B. Wang, Holographic parity violating charged fluid dual to Chern-Simons modified gravity, Phys. Rev. D 89 (2014) 064036 [arXiv:1306.5486] [INSPIRE].
H. Liu, H. Ooguri, B. Stoica and N. Yunes, Spontaneous Generation of Angular Momentum in Holographic Theories, Phys. Rev. Lett. 110 (2013) 211601 [arXiv:1212.3666] [INSPIRE].
H. Liu, H. Ooguri and B. Stoica, Angular Momentum Generation by Parity Violation, Phys. Rev. D 89 (2014) 106007 [arXiv:1311.5879] [INSPIRE].
H. Liu, H. Ooguri and B. Stoica, Hall Viscosity and Angular Momentum in Gapless Holographic Models, Phys. Rev. D 90 (2014) 086007 [arXiv:1403.6047] [INSPIRE].
F. Wilczek, Two Applications of Axion Electrodynamics, Phys. Rev. Lett. 58 (1987) 1799 [INSPIRE].
S.M. Carroll, G.B. Field and R. Jackiw, Limits on a Lorentz and Parity Violating Modification of Electrodynamics, Phys. Rev. D 41 (1990) 1231 [INSPIRE].
R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68 (2003) 104012 [gr-qc/0308071] [INSPIRE].
D.T. Son and C. Wu, Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum, JHEP 07 (2014) 076 [arXiv:1311.4882] [INSPIRE].
S.S. Gubser, Colorful horizons with charge in anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].
M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].
S. Alexander and N. Yunes, Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1 [arXiv:0907.2562] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].
E. Barnes, D. Vaman, C. Wu and P. Arnold, Real-time finite-temperature correlators from AdS/CFT, Phys. Rev. D 82 (2010) 025019 [arXiv:1004.1179] [INSPIRE].
P. Arnold, D. Vaman, C. Wu and W. Xiao, Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT, JHEP 10 (2011) 033 [arXiv:1105.4645] [INSPIRE].
N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [INSPIRE].
B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.6368
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Wu, C. Angular momentum generation from holographic Chern-Simons models. J. High Energ. Phys. 2014, 90 (2014). https://doi.org/10.1007/JHEP12(2014)090
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)090