Abstract
We construct the three-dimensional effective field theory which reproduces low-momentum static correlation functions in four-dimensional quantum field theories with U(1) axial anomalies and a dynamical vector gauge field, in thermal equilibrium. We compute radiative corrections to parity-violating chiral conductivities, to leading order in the effective theory. All of the anomaly-induced transport is susceptible to radiative corrections, except for certain two-point functions which are required by symmetry to vanish.
Similar content being viewed by others
References
S. Weinberg, The quantum theory of fields. Volume 2: modern applications, Cambridge University Press, Cambridge U.K. (1996) [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009)191601 [arXiv:0906.5044] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011)023 [arXiv:1011.5107] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
D. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [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].
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].
A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
A.Y. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81 (1998) 3503 [cond-mat/9803346] [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008)074033 [arXiv:0808.3382] [INSPIRE].
D.E. Kharzeev and H.J. Warringa, Chiral magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].
A. Vilenkin, Cancellation of equilibrium parity violating currents, Phys. Rev. D 22 (1980) 3067 [INSPIRE].
M.A. Metlitski and A.R. Zhitnitsky, Anomalous axion interactions and topological currents in dense matter, Phys. Rev. D 72 (2005) 045011 [hep-ph/0505072] [INSPIRE].
G. Newman and D. Son, Response of strongly-interacting matter to magnetic field: some exact results, Phys. Rev. D 73 (2006) 045006 [hep-ph/0510049] [INSPIRE].
A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].
V.I. Zakharov, Chiral magnetic effect in hydrodynamic approximation, Lect. Notes Phys. 871 (2013)295 [arXiv:1210.2186] [INSPIRE].
S.L. Adler and W.A. Bardeen, Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev. 182 (1969) 1517 [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
S.L. Adler, Anomalies to all orders, hep-th/0405040 [INSPIRE].
S. Golkar and D.T. Son, Non-renormalization of the chiral vortical effect coefficient, arXiv:1207.5806 [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].
P. Kovtun, G.D. Moore and P. Romatschke, The stickiness of sound: an absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics, Phys. Rev. D 84 (2011)025006 [arXiv:1104.1586] [INSPIRE].
E. Braaten and A. Nieto, Effective field theory approach to high temperature thermodynamics, Phys. Rev. D 51 (1995) 6990 [hep-ph/9501375] [INSPIRE].
E. Braaten and A. Nieto, Free energy of QCD at high temperature, Phys. Rev. D 53 (1996) 3421 [hep-ph/9510408] [INSPIRE].
J.O. Andersen, The free energy of high temperature QED to order e 5 from effective field theory, Phys. Rev. D 53 (1996) 7286 [hep-ph/9509409] [INSPIRE].
K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012)101601 [arXiv:1203.3556] [INSPIRE].
A. Niemi and G. Semenoff, Axial anomaly induced Fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett. 51 (1983) 2077 [INSPIRE].
A. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].
S.R. Coleman and B.R. Hill, No more corrections to the topological mass term in QED in three-dimensions, Phys. Lett. B 159 (1985) 184 [INSPIRE].
J.C. Collins, A.V. Manohar and M.B. Wise, Renormalization of the vector current in QED, Phys. Rev. D 73 (2006) 105019 [hep-th/0512187] [INSPIRE].
V. Rubakov, On chiral magnetic effect and holography, arXiv:1005.1888 [INSPIRE].
V. Braguta, M. Chernodub, K. Landsteiner, M. Polikarpov and M. Ulybyshev, Numerical evidence of the axial magnetic effect, arXiv:1303.6266 [INSPIRE].
H. Itoyama and A.H. Mueller, The axial anomaly at finite temperature, Nucl. Phys. B 218 (1983)349 [INSPIRE].
R.A. Bertlmann, Anomalies in quantum field theory, Clarendon Press, Oxford U.K. (1996) [INSPIRE].
J.A. Harvey, TASI 2003 lectures on anomalies, hep-th/0509097 [INSPIRE].
A. Bilal, Lectures on anomalies, arXiv:0802.0634 [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971)95 [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
L.D. Landau and E.M. Lifshitz, Fluid mechanics, Pergamon Press, Oxford U.K. (1987).
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
E. Wang and U.W. Heinz, A generalized fluctuation dissipation theorem for nonlinear response functions, Phys. Rev. D 66 (2002) 025008 [hep-th/9809016] [INSPIRE].
G.D. Moore and K.A. Sohrabi, Kubo formulae for second-order hydrodynamic coefficients, Phys. Rev. Lett. 106 (2011) 122302 [arXiv:1007.5333] [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].
K. Jensen et al., Parity-violating hydrodynamics in 2 + 1 dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [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].
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].
T. Evans, N point finite temperature expectation values at real times, Nucl. Phys. B 374 (1992)340 [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [INSPIRE].
R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [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].
S. Bhattacharyya, J.R. David and S. Thakur, Second order transport from anomalies, arXiv:1305.0340 [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [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].
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].
I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett. 56 (1986) 746 [INSPIRE].
S.N. Solodukhin, Entanglement entropy of black holes, Living Rev. Rel. 14 (2011) 8 [arXiv:1104.3712] [INSPIRE].
R. Loganayagam, Anomalies and the helicity of the thermal state, arXiv:1211.3850 [INSPIRE].
J.I. Kapusta, Bose-Einstein condensation, spontaneous symmetry breaking and gauge theories, Phys. Rev. D 24 (1981) 426 [INSPIRE].
P.A. Davidson, An introduction to magnetohydrodynamics, Cambridge University Press, Cambridge U.K. (2001).
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
A. Redlich and L. Wijewardhana, Induced Chern-Simons terms at high temperatures and finite densities, Phys. Rev. Lett. 54 (1985) 970 [INSPIRE].
A. Niemi and G. Semenoff, A comment on ‘induced Chern-Simons terms at high temperatures and finite densities’, Phys. Rev. Lett. 54 (1985) 2166 [INSPIRE].
Z. Khaidukov, V. Kirilin, A. Sadofyev and V. Zakharov, On magnetostatics of chiral media, arXiv:1307.0138 [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].
Y. Akamatsu and N. Yamamoto, Chiral plasma instabilities, Phys. Rev. Lett. 111 (2013) 052002 [arXiv:1302.2125] [INSPIRE].
D. Hou, H. Liu and H.-C. Ren, Some field theoretic issues regarding the chiral magnetic effect, JHEP 05 (2011) 046 [arXiv:1103.2035] [INSPIRE].
H.J. Warringa, Dynamics of the chiral magnetic effect in a weak magnetic field, Phys. Rev. D 86 (2012) 085029 [arXiv:1205.5679] [INSPIRE].
X.-G. Huang, A. Sedrakian and D.H. Rischke, Kubo formulae for relativistic fluids in strong magnetic fields, Annals Phys. 326 (2011) 3075 [arXiv:1108.0602] [INSPIRE].
D. Marolf and S.F. Ross, Boundary conditions and new dualities: vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].
K. Jensen, Chiral anomalies and AdS/CMT in two dimensions, JHEP 01 (2011) 109 [arXiv:1012.4831] [INSPIRE].
E. Gorbar, V. Miransky, I. Shovkovy and X. Wang, Radiative corrections to chiral separation effect in QED, Phys. Rev. D 88 (2013) 025025 [arXiv:1304.4606] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1307.3234
Rights and permissions
About this article
Cite this article
Jensen, K., Kovtun, P. & Ritz, A. Chiral conductivities and effective field theory. J. High Energ. Phys. 2013, 186 (2013). https://doi.org/10.1007/JHEP10(2013)186
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)186