Skip to main content
Log in

Anomaly/transport in an Ideal Weyl gas

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study some of the transport processes which are specific to an ideal gas of relativistic Weyl fermions and relate the corresponding transport coefficients to various anomaly coefficients of the system. We propose that these transport processes can be thought of as arising from the continuous injection of chiral states and their subsequent adiabatic flow driven by vorticity. This in turn leads to an elegant expression relating the anomaly induced transport coefficients to the anomaly polynomial of the Ideal Weyl gas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.T. Son and P. Surówka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, Phys. Rev. D 84 (2011) 045025 [arXiv:1105.6360] [INSPIRE].

    ADS  Google Scholar 

  4. R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [INSPIRE].

  5. I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].

    Article  ADS  Google Scholar 

  6. P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla, Large rotating AdS black holes from fluid mechanics, JHEP 09 (2008) 054 [arXiv:0708.1770] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].

    Article  ADS  Google Scholar 

  9. J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Torabian and H.-U. Yee, Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries, JHEP 08 (2009) 020 [arXiv:0903.4894] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. 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].

    Article  ADS  Google Scholar 

  12. Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. L. Bonora, M. Cvitan, P. Dominis Prester, S. Pallua and I. Smolic, Gravitational Chern-Simons Lagrangians and black hole entropy, JHEP 07 (2011) 085 [arXiv:1104.2523] [INSPIRE].

    Article  ADS  Google Scholar 

  14. A. Cappelli, M. Huerta and G.R. Zemba, Thermal transport in chiral conformal theories and hierarchical quantum Hall states, Nucl. Phys. B 636 (2002) 568 [cond-mat/0111437] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Vilenkin, Parity violating currents in thermal radiation, Phys. Lett. B 80 (1978) 150 [INSPIRE].

    ADS  Google Scholar 

  16. A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].

    ADS  Google Scholar 

  18. A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [INSPIRE].

    ADS  Google Scholar 

  19. A. Vilenkin, Cancellation of equilibrium parity violating currents, Phys. Rev. D 22 (1980) 3067 [INSPIRE].

    ADS  Google Scholar 

  20. A. Vilenkin, Parity nonconservation and neutrino transport in magnetic fields, Astrophys. J. 451 (1995) 700 [INSPIRE].

    Article  ADS  Google Scholar 

  21. K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].

    ADS  Google Scholar 

  22. D.E. Kharzeev and H.J. Warringa, Chiral magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].

    ADS  Google Scholar 

  23. K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].

    Article  ADS  Google Scholar 

  24. F.D. Haldane, Berry curvature on the Fermi surface: anomalous hall effect as a topological Fermi-liquid property, Phys. Rev. Lett. 93 (2004) 206602 [cond-mat/0408417].

    Article  ADS  Google Scholar 

  25. D. Xiao, M.-C. Chang and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82 (2010) 1959 [arXiv:0907.2021] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. X. Wan, A.M. Turner, A. Vishwanath and S.Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83 (2011) 205101 [arXiv:1007.0016] [INSPIRE].

    ADS  Google Scholar 

  27. K.-Y. Yang, Y.-M. Lu and Y. Ran, Quantum Hall effects in a Weyl semimetal: possible application in pyrochlore iridates, Phys. Rev. B 84 (2011) 075129 [arXiv:1105.2353] [INSPIRE].

    ADS  Google Scholar 

  28. S. Ryu, J.E. Moore and A.W. Ludwig, Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors, Phys. Rev. B 85 (2012) 045104 [arXiv:1010.0936] [INSPIRE].

    ADS  Google Scholar 

  29. 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].

    Article  ADS  Google Scholar 

  30. S. Dubovsky, L. Hui and A. Nicolis, Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, arXiv:1107.0732 [INSPIRE].

  31. K.-c. Chou, Z.-b. Su, B.-l. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. G.D. Moore and K.A. Sohrabi, Kubo formulae for second-order hydrodynamic coefficients, Phys. Rev. Lett. 106 (2011) 122302 [arXiv:1007.5333] [INSPIRE].

    Article  ADS  Google Scholar 

  33. 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].

    ADS  Google Scholar 

  34. 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].

    MathSciNet  ADS  Google Scholar 

  35. O. Saremi and K.A. Sohrabi, Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT, JHEP 11 (2011) 147 [arXiv:1105.4870] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. P. Arnold and D. Vaman, 4-point correlators in finite-temperature AdS/CFT: jet quenching correlations, JHEP 11 (2011) 033 [arXiv:1109.0040] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  37. R. Loganayagam, Entropy current in conformal hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press, Cambridge U.K. (1996).

    Google Scholar 

  39. R. Bertlmann, International Series of Monographs on Physics. Vol. 91: Anomalies in quantum field theory, Oxford University Press, Oxford U.K. (1996).

    Google Scholar 

  40. F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press, Cambridge U.K. (2006).

    Book  MATH  Google Scholar 

  41. J.A. Harvey, TASI 2003 lectures on anomalies, hep-th/0509097 [INSPIRE].

  42. A. Bilal, Lectures on anomalies, arXiv:0802.0634 [INSPIRE].

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Piotr Surówka.

Additional information

ArXiv ePrint: 1201.2812

Rights and permissions

Reprints and permissions

About this article

Cite this article

Loganayagam, R., Surówka, P. Anomaly/transport in an Ideal Weyl gas. J. High Energ. Phys. 2012, 97 (2012). https://doi.org/10.1007/JHEP04(2012)097

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2012)097

Keywords

Navigation