Abstract
Using the anomaly inflow mechanism, we compute the flavor/Lorentz non-invariant contribution to the partition function in a background with a U(1) isometry. This contribution is a local functional of the background fields. By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed. Our result is in line with, and an extension of, previous studies on the role of anomalies in a hydrodynamic setting. Along the way we find simplified expressions for Bardeen-Zumino polynomials and various transgression formulae.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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 et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
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].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
D.E. Kharzeev and H.J. Warringa, Chiral Magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].
M. Lublinsky and I. Zahed, Anomalous Chiral Superfluidity, Phys. Lett. B 684 (2010) 119 [arXiv:0910.1373] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [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].
R. Loganayagam, Anomaly Induced Transport in Arbitrary Dimensions, arXiv:1106.0277 [INSPIRE].
Y. Neiman and Y. Oz, Anomalies in Superfluids and a Chiral Electric Effect, JHEP 09 (2011) 011 [arXiv:1106.3576] [INSPIRE].
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].
T. Kimura and T. Nishioka, The Chiral Heat Effect, Prog. Theor. Phys. 127 (2012) 1009 [arXiv:1109.6331] [INSPIRE].
S. Lin, An anomalous hydrodynamics for chiral superfluid, Phys. Rev. D 85 (2012) 045015 [arXiv:1112.3215] [INSPIRE].
J.-H. Gao, Z.-T. Liang, S. Pu, Q. Wang and X.-N. Wang, Chiral Anomaly and Local Polarization Effect from Quantum Kinetic Approach, Phys. Rev. Lett. 109 (2012) 232301 [arXiv:1203.0725] [INSPIRE].
N. Banerjee et al., Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen, Triangle Anomalies, Thermodynamics and Hydrodynamics, Phys. Rev. D 85 (2012) 125017 [arXiv:1203.3599] [INSPIRE].
S. Jain and T. Sharma, Anomalous charged fluids in 1 + 1d from equilibrium partition function, JHEP 01 (2013) 039 [arXiv:1203.5308] [INSPIRE].
M. Valle, Hydrodynamics in 1 + 1 dimensions with gravitational anomalies, JHEP 08 (2012) 113 [arXiv:1206.1538] [INSPIRE].
S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions, JHEP 01 (2013) 040 [arXiv:1206.6106] [INSPIRE].
S. Golkar and D.T. Son, Non-Renormalization of the Chiral Vortical Effect Coefficient, arXiv:1207.5806 [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
J.-W. Chen, S. Pu, Q. Wang and X.-N. Wang, Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation, Phys. Rev. Lett. 110 (2013) 262301 [arXiv:1210.8312] [INSPIRE].
J.L. Manes and M. Valle, Parity violating gravitational response and anomalous constitutive relations, JHEP 01 (2013) 008 [arXiv:1211.0876] [INSPIRE].
R. Loganayagam, Anomalies and the Helicity of the Thermal State, JHEP 11 (2013) 205 [arXiv:1211.3850] [INSPIRE].
S. Bhattacharyya, J.R. David and S. Thakur, Second order transport from anomalies, JHEP 01 (2014) 010 [arXiv:1305.0340] [INSPIRE].
M. Valle, Kinetic theory and evolution of cosmological fluctuations with neutrino number asymmetry, Phys. Rev. D 88 (2013) 041304 [arXiv:1307.0392] [INSPIRE].
E. Megias and F. Pena-Benitez, Fluid/Gravity Correspondence, Second Order Transport and Gravitational Anomaly, EPJ Web of Conferences 66 (2014) 04018 [arXiv:1307.7592] [INSPIRE].
X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83 (2011) 1057 [arXiv:1008.2026].
D.E. Kharzeev and D.T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106 (2011) 062301 [arXiv:1010.0038] [INSPIRE].
K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [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].
K. Jensen, P. Kovtun and A. Ritz, Chiral conductivities and effective field theory, JHEP 10 (2013) 186 [arXiv:1307.3234] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
D.-F. Hou, H. Liu and H.-c. Ren, A Possible Higher Order Correction to the Vortical Conductivity in a Gauge Field Plasma, Phys. Rev. D 86 (2012) 121703 [arXiv:1210.0969] [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and Covariant Anomalies in Gauge and Gravitational Theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [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].
C.G. Callan Jr. and J.A. Harvey, Anomalies and fermion zero modes on strings and domain walls, Nucl. Phys. B 250 (1985) 427 [INSPIRE].
M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Polon. 6 (1937) 163 [INSPIRE].
A. Papapetrou, Spinning test particles in general relativity. 1., Proc. Roy. Soc. Lond. A 209 (1951) 248 [INSPIRE].
W.G. Dixon, Dynamics of extended bodies in general relativity. I. Momentum and angular momentum, Proc. Roy. Soc. Lond. A 314 (1970) 499 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of Gauge Theories, Annals Phys. 98 (1976) 287 [INSPIRE].
R. Stora, Algebraic structure and topological origin of anomalies, at Cargese Summer Institute: Progress in Gauge Field Theory, Cargese France (1983).
B. Zumino, Y.-S. Wu and A. Zee, Chiral Anomalies, Higher Dimensions and Differential Geometry, Nucl. Phys. B 239 (1984) 477 [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].
L.D. Landau and E.M. Lifshits, Fluid mechanics, Pergamon Press, Oxford U.K. (1987).
K. Jensen et al., Parity-violating hydrodynamics in 2 + 1 dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [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].
M. Stone, Gravitational Anomalies and Thermal Hall effect in Topological Insulators, Phys. Rev. B 85 (2012) 184503 [arXiv:1201.4095] [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: 1310.7024
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Jensen, K., Loganayagam, R. & Yarom, A. Anomaly inflow and thermal equilibrium. J. High Energ. Phys. 2014, 134 (2014). https://doi.org/10.1007/JHEP05(2014)134
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2014)134