Abstract
In this paper, based on the principles of linear response theory, we compute the longitudinal DC conductivity associated with Lifshitz like fixed points in the presence of chiral anomalies in (3 + 1) dimensions. In our analysis, apart from having the usual anomalous contributions due to chiral anomaly, we observe an additional and pure parity odd effect to the magnetoconductivity which has its origin in the broken Lorentz (boost) invariance at a Lifshitz fixed point. We also device a holographic set up in order to compute (z = 2) Lifshitz contributions to the magnetoconductivity precisely at strong coupling and low charge density limit.
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References
R.A. Bertlmann, Anomalies in quantum field theory, International series of monographs on physics 91, Clarendon, Oxford U.K. (1996) [INSPIRE].
F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge Univ. Pr.. Cambridge U.K. (2006) [INSPIRE].
K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies, Clarendon, Oxford U.K. (2004) [INSPIRE].
L.D. Landau and E.M. Lifshitz, Fluid mechanics, second edition, Butterworth-Heinemann, Oxford U.K. (1987).
A. Yu. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81 (1998) 3503 [cond-mat/9803346] [INSPIRE].
G.M. Newman and D.T. Son, Response of strongly-interacting matter to magnetic field: some exact results, Phys. Rev. D 73 (2006) 045006 [hep-ph/0510049] [INSPIRE].
G.M. Newman, Anomalous hydrodynamics, JHEP 01 (2006) 158 [hep-ph/0511236] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous transport from Kubo formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].
S. Bhattacharyya, J.R. David and S. Thakur, Second order transport from anomalies, JHEP 01 (2014) 010 [arXiv:1305.0340] [INSPIRE].
K. Landsteiner and L. Melgar, Holographic flow of anomalous transport coefficients, JHEP 10 (2012) 131 [arXiv:1206.4440] [INSPIRE].
S. Bhattacharyya, Entropy current from partition function: one example, JHEP 07 (2014) 139 [arXiv:1403.7639] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE].
R. Loganayagam and P. Surowka, Anomaly/transport in an ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].
I. Amado, N. Lisker and A. Yarom, Universal chiral conductivities for low temperature holographic superfluids, JHEP 06 (2014) 084 [arXiv:1401.5795] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
K. Landsteiner, Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B 89 (2014) 075124 [arXiv:1306.4932] [INSPIRE].
R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [INSPIRE].
T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].
I. Gahramanov, T. Kalaydzhyan and I. Kirsch, Anisotropic hydrodynamics, holography and the chiral magnetic effect, Phys. Rev. D 85 (2012) 126013 [arXiv:1203.4259] [INSPIRE].
R. Banerjee, S. Dey and B.R. Majhi, Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters, Phys. Rev. D 92 (2015) 044019 [arXiv:1412.5878] [INSPIRE].
R. Banerjee, P. Chakraborty, S. Dey, B.R. Majhi and A.K. Mitra, Two dimensional hydrodynamics with gauge and gravitational anomalies, Phys. Rev. D 89 (2014) 104013 [arXiv:1307.1313] [INSPIRE].
R. Banerjee, Exact results in two dimensional chiral hydrodynamics with gravitational anomalies, Eur. Phys. J. C 74 (2014) 2824 [arXiv:1303.5593] [INSPIRE].
B.R. Majhi, Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid, JHEP 03 (2014) 001 [arXiv:1401.1074] [INSPIRE].
B.R. Majhi, Vacuum condition and the relation between response parameter and anomaly coefficient in (1 + 3) dimensions, JHEP 08 (2014) 045 [arXiv:1405.4634] [INSPIRE].
R. Banerjee and S. Dey, Constitutive relations and response parameters in two dimensional hydrodynamics with gauge and gravitational anomalies, Phys. Lett. B 733 (2014) 198 [arXiv:1403.7357] [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
D.E. Kharzeev and H.J. Warringa, Chiral magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in Holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].
A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic anomalous conductivities and the chiral magnetic effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic gravitational anomaly and chiral vortical effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalies and transport coefficients: the chiral gravito-magnetic effect, arXiv:1110.3615 [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Gravitational anomaly and hydrodynamics, J. Phys. Conf. Ser. 343 (2012) 012073 [arXiv:1111.2823] [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Gravitational anomaly and hydrodynamics in AdS/CFT, Fortsch. Phys. 60 (2012) 1064 [INSPIRE].
E. Megias, K. Landsteiner and F. Pena-Benitez, Fluid/gravity correspondence and holographic mixed gauge-gravitational anomaly, Acta Phys. Polon. Supp. 6 (2013) 45 [INSPIRE].
H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
K.-S. Kim, H.-J. Kim and M. Sasaki, Anomalous transport in Weyl metal: a Boltzmann-equation approach, arXiv:1402.4240 [INSPIRE].
H.-J. Kim et al., Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena, Phys. Rev. Lett. 111 (2013) 246603 [arXiv:1307.6990] [INSPIRE].
K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].
A. Jimenez-Alba, K. Landsteiner, Y. Liu and Y.-W. Sun, Anomalous magnetoconductivity and relaxation times in holography, JHEP 07 (2015) 117 [arXiv:1504.06566] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Lifshitz hydrodynamics, JHEP 11 (2013) 145 [arXiv:1304.7481] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Lifshitz field theories at non-zero temperature, hydrodynamics and gravity, JHEP 03 (2014) 029 [arXiv:1309.6794] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Bulk viscosity in holographic Lifshitz hydrodynamics, JHEP 03 (2014) 050 [arXiv:1312.6380] [INSPIRE].
S. Chapman, C. Hoyos and Y. Oz, Lifshitz superfluid hydrodynamics, JHEP 07 (2014) 027 [arXiv:1402.2981] [INSPIRE].
C. Eling and Y. Oz, Hořava-Lifshitz black hole hydrodynamics, JHEP 11 (2014) 067 [arXiv:1408.0268] [INSPIRE].
C. Hoyos, A. Meyer and Y. Oz, Parity breaking transport in Lifshitz hydrodynamics, JHEP 09 (2015) 031 [arXiv:1505.03141] [INSPIRE].
D.V. Khveshchenko, Taking a critical look at holographic critical matter, arXiv:1404.7000 [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, arXiv:1110.3814 [INSPIRE].
B. Chen and Q.-G. Huang, Field theory at a Lifshitz point, Phys. Lett. B 683 (2010) 108 [arXiv:0904.4565] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
D.-W. Pang, Conductivity and diffusion constant in Lifshitz backgrounds, JHEP 01 (2010) 120 [arXiv:0912.2403] [INSPIRE].
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Roychowdhury, D. Magnetoconductivity in chiral Lifshitz hydrodynamics. J. High Energ. Phys. 2015, 145 (2015). https://doi.org/10.1007/JHEP09(2015)145
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DOI: https://doi.org/10.1007/JHEP09(2015)145