As the experiments indicate, not only the chiral anomaly but also the gravitational anomaly exist in Weyl semimetal. Gravitational anomaly induces the chiral vortical effect. Hence it is necessary to study the chiral vortical effect in Weyl semimetal. Furthermore, due to the analogy to the graphene, Weyl semimetal may also suffer strong coupling. Based on this, we study the chiral vortical conductivity in a strong coupling Weyl semimetal by AdS/CFT. Under the circumstance where only gravitational anomaly is considered, we obtain the conclusions as follows. 1)Gravitational anomaly induces the chiral vortical effect, which exists in the Weyl semimetal equipped with the chiral fermions, and it is proportional to the coupling strength. 2)Chiral vortical conductivity is proportional to square of temperature.
[1] Wan X G, Turner A M, Vishwanath A, et al. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates[J]. Physical Review B, 2011, 83(20):205 101.
[2] Weng H M, Fang C, Fang Z, et al. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides[J].Physical Review X, 2015, 5(1):011 029.
[3] Son D T, Yamamoto N. Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids[J]. Physical Review Letter, 2012, 109(18):181 602.
[4] Gooth J, Niemann A C, Meng T, et al. Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP[J].Nature, 2017, 547:324-327.
[5] Müller M, Sachdev S. Collective cyclotron motion of the relativistic plasma in graphene[J].Physical Review B, 2008, 78(11):115 419.
[6] Müller M, Fritz L, Sachdev S. Quantum-critical relativistic magnetotransport in graphene[J]. Physical Review B, 2008, 78(11):115 406.
[7] Crossno J, Shi J K, Wang K, et al. Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene[J]. Science,2016, 351:1 058-1 061.
[8] Ghahari F, Xie H Y, Taniguch T, et al. Enhanced thermoelectric power in graphene:violation of the Mott relation by Inelastic scattering[J]. Physical Review Letter, 2016, 116(13):136 802.
[9] Lucas A, Crossno J, Fong K C, et al. Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene[J]. Physical Review B, 2016, 93(7):075 426.
[10] Lucas A. Sound waves and resonances in electron-hole plasma[J]. Physical Review B, 2016, 93(24):245 153.
[11] Lucas A, Davison R A, Sachdev S. Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals[J]. Proceedings of the National Academy of Sciences, 2016, 113(34):9 463-9 468.
[12] Landsteiner K, Liu Y. The holographic Weyl semi-metal[J]. Physics Letters B, 2016, 753:453-457.
[13] Sun Y W, Yang Q. Negative magnetoresistivity in holography[J].Journal of High Energy Physics,2016,1609:122.
[14] Landsteiner K, Liu Y, Sun Y W. Odd viscosity in the quantum critical region of a holographic Weyl semimetal[J].Physical Review Letter, 2016, 117(8):081 604.
[15] Ammon M, Grieninger S, Jimenez-Alba A, et al. Holographic quenches and anomalous transport[J]. Journal of High Energy Physics, 2016, 1609:131.
[16] Copetti C, Fernández-Pendás J,Landsteiner K. Axial Hall effect and universality of holographic Weyl semimetals[J]. Journal of High Energy Physics, 2017, 1702:138.
[17] Grignani G, Marini A, Pena-Benitez F, et al. AC conductivity for a holographic Weyl semimetal[J].Journal of High Energy Physics, 2017, 1703:125.
[18] Ammon M, Heinrich M, Jiménez-Alba A, et al. Surface States in Holographic Weyl Semimetals[J].Physical Review Letter, 2017, 118(20):201 601.
[19] Landsteiner K, Megias E, Melgar L, et al. Holographic gravitational anomaly and chiral vortical effect[J]. Journal of High Energy Physics, 2011, 1109:121.
[20] Kharzeev D E, Warringa H J. Chiral magnetic conductivity[J]. Physical Review D, 2009, 80(3):034 028.
[21] Hou D, Liu H, Ren H C. Some field theoretic issues regarding the chiral magnetic effect[J]. Journal of High Energy Physics, 2011, 1105:046.
[22] Erdmenger J, Haack M, Kaminski M, et al. Fluid dynamics of R-charged black holes[J]. Journal of High Energy Physics, 2009, 0901:055.
[23] Banerjee N, Bhattacharya J, Bhattacharyya S, et al. Hydrodynamics from charged black branes[J]. Journal of High Energy Physics, 2011, 1101:094.
[24] Kharzeev D E, Warringa H J. Cancellation of equilibrium parity-violating currents[J]. Physical Review D, 1980, 22(12):3 067.
[25] Son D T, Surowka P. Hydrodynamics with triangle anomalies[J].Physical Review Letter, 2009, 103(19):191 601.
[26] Neiman Y, Oz Y. Relativistic hydrodynamics with general anomalous charges[J]. Journal of High Energy Physics, 2011, 1103:023.
[27] Amado I, Landsteiner K, Pena-Benitez F. Anomalous ransport coefficients from Kubo formulas in Holography[J].Journal of High Energy Physics, 2011, 1105:081.
[28] Landsteiner K, Megias E, Pena-Benitez F. Gravitational anomaly and transport phenomena[J]. Physical Review Letter, 2011, 107(02):021 601.
[29] Jensen K, Kaminski M, Kovtun P, et al. Towards hydrodynamics without an entropy current[J].Physical Review Letter, 2012, 109(10):101 601.
[30] Colladay D, Kostelecky V A. Lorentz-violating extension of the standard model[J]. Physical Review D, 1998, 58(11):116 002.
[31] Gubser S S, Klebanov I R, Polyakov A M. Gauge theory correlators from noncritical string theory[J]. Physics Letters B, 1998, 428:105.
