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Conformal anomalies in hydrodynamics

  • Christopher ElingEmail author
  • Yaron Oz
  • Stefan Theisen
  • Shimon Yankielowicz
Article

Abstract

We study the effect of conformal anomalies on the hydrodynamic description of conformal field theories in even spacetime dimensions. We consider equilibrium curved backgrounds characterized by a time-like Killing vector and construct a local low energy effective action that captures the conformal anomalies. Using as a special background the Rindler spacetime we derive a formula for the anomaly effect on the hydrodynamic pressure. We find that this anomalous effect is only due to the Euler central charge.

Keywords

Anomalies in Field and String Theories Conformal and W Symmetry Holography and quark-gluon plasmas 

References

  1. [1]
    L.D. Landau and E.M. Lifshitz, Fluid mechanics, Butterworth-Heinemann, U.K. (2000).Google Scholar
  2. [2]
    J. Erdmenger and H. Osborn, Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].MathSciNetADSGoogle Scholar
  4. [4]
    S. Deser, Closed form effective conformal anomaly actions in D ≥ 4, Phys. Lett. B 479 (2000) 315 [hep-th/9911129] [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].MathSciNetADSGoogle Scholar
  6. [6]
    A. Schwimmer and S. Theisen, Spontaneous breaking of conformal invariance and trace anomaly matching, Nucl. Phys. B 847 (2011) 590 [arXiv:1011.0696] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    H. Bloete, J.L. Cardy and M. Nightingale, Conformal invariance, the central charge and universal finite size amplitudes at criticality, Phys. Rev. Lett. 56 (1986) 742 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett. 56 (1986) 746 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    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].ADSCrossRefGoogle Scholar
  18. [18]
    S. Chapman, Y. Neiman and Y. Oz, Fluid/gravity correspondence, local Wald entropy current and gravitational anomaly, JHEP 07 (2012) 128 [arXiv:1202.2469] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N. Banerjee et al., Constraints on fluid dynamics from equilibrium partition functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D.V. Fursaev and G. Miele, Cones, spins and heat kernels, Nucl. Phys. B 484 (1997) 697 [hep-th/9605153] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    W.G. Unruh and N. Weiss, Acceleration radiation in interacting field theories, Phys. Rev. D 29 (1984) 1656 [INSPIRE].MathSciNetADSGoogle Scholar
  23. [23]
    W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    G. Basar, D. Kharzeev, D. Kharzeev and V. Skokov, Conformal anomaly as a source of soft photons in heavy ion collisions, Phys. Rev. Lett. 109 (2012) 202303 [arXiv:1206.1334] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    R. Loganayagam, Entropy current in conformal hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    H. Elvang et al., On renormalization group flows and the a-theorem in 6D, JHEP 10 (2012) 011 [arXiv:1205.3994] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Christopher Eling
    • 1
    Email author
  • Yaron Oz
    • 2
  • Stefan Theisen
    • 1
  • Shimon Yankielowicz
    • 2
  1. 1.Max Planck Institute for Gravitational Physics, Albert Einstein InstitutePotsdamGermany
  2. 2.Raymond and Beverly Sackler School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

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