Abstract
We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid. We see that there are 27 parity odd transport coefficients, of which 12 are non-vanishing in equilibrium. We use the equilibrium partition function method to express 7 of these in terms of the anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The remaining 5 are constrained by 3 relations which also involve the anomaly. We derive Kubo formulae for 2 of the transport coefficients and show these agree with that derived from the equilibrium partition function.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
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].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
R. Loganayagam and P. Surowka, Anomaly/Transport in an Ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].
K. Jensen, Triangle Anomalies, Thermodynamics and Hydrodynamics, Phys. Rev. D 85 (2012) 125017 [arXiv:1203.3599] [INSPIRE].
N. Banerjee, S. Dutta, S. Jain, R. Loganayagam and T. Sharma, Constraints on Anomalous Fluid in Arbitrary Dimensions, JHEP 03 (2013) 048 [arXiv:1206.6499] [INSPIRE].
R. Loganayagam, Anomalies and the Helicity of the Thermal State, JHEP 11 (2013) 205 [arXiv:1211.3850] [INSPIRE].
V. Nair, R. Ray and S. Roy, Fluids, Anomalies and the Chiral Magnetic Effect: A Group-Theoretic Formulation, Phys. Rev. D 86 (2012) 025012 [arXiv:1112.4022] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].
P. Romatschke and D.T. Son, Spectral sum rules for the quark-gluon plasma, Phys. Rev. D 80 (2009) 065021 [arXiv:0903.3946] [INSPIRE].
A.V. Andreev, D.T. Son and B. Spivak, Hydrodynamics of liquids of chiral molecules and suspensions containing chiral particles, Phys. Rev. Lett. 104 (2010) 198301.
B. Sahoo and H.-U. Yee, Holographic chiral shear waves from anomaly, Phys. Lett. B 689 (2010) 206 [arXiv:0910.5915] [INSPIRE].
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].
N. Banerjee et al., Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [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].
E. Megias and F. Pena-Benitez, Holographic Gravitational Anomaly in First and Second Order Hydrodynamics, JHEP 05 (2013) 115 [arXiv:1304.5529] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [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: 1305.0340
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Bhattacharyya, S., David, J.R. & Thakur, S. Second order transport from anomalies. J. High Energ. Phys. 2014, 10 (2014). https://doi.org/10.1007/JHEP01(2014)010
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2014)010