Abstract
In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the energy current. We also point out that the anomalous vortical conductivity can be understood as a response to a gravitomagnetic field. We apply these Kubo formulas to a simple holographic system, the R-charged black hole.
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References
A. Deshpande et al., Workshop on P- and CP-odd Effects in Hot and Dense Matter, Brookhaven National Laboratory, RIKEN Research Center Workshop, April 2010.
A.Y. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, cond-mat/9803346 [SPIRES].
M. Giovannini and M.E. Shaposhnikov, Primordial hypermagnetic fields and triangle anomaly, Phys. Rev. D 57 (1998) 2186 [hep-ph/9710234] [SPIRES].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ’Event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [SPIRES].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [SPIRES].
D.E. Kharzeev and H.J. Warringa, Chiral Magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [SPIRES].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, Real-time dynamics of the Chiral Magnetic Effect, Phys. Rev. Lett. 104 (2010) 212001 [arXiv:1002.2495] [SPIRES].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, Electric-current Susceptibility and the Chiral Magnetic Effect, Nucl. Phys. A 836 (2010) 311 [arXiv:0912.2961] [SPIRES].
B. Müller and A. Schafer, Charge Fluctuations from the Chiral Magnetic Effect in Nuclear Collisions, Phys. Rev. C 82 (2010) 057902 [arXiv:1009.1053] [SPIRES].
V.D. Orlovsky and V.I. Shevchenko, Towards a quantum theory of chiral magnetic effect, Phys. Rev. D 82 (2010) 094032 [arXiv:1008.4977] [SPIRES].
S. Pu, J.-h. Gao and Q. Wang, A consistent description of kinetic equation with triangle anomaly, arXiv:1008.2418 [SPIRES].
S.-i. Nam, Vector current correlation and charge separation via chiral magnetic effect, Phys. Rev. D 82 (2010) 045017 [arXiv:1004.3444] [SPIRES].
W.-j. Fu, Y.-x. Liu and Y.-l. Wu, Chiral Magnetic Effect and QCD Phase Transitions with Effective Models, arXiv:1003.4169 [SPIRES].
M. Asakawa, A. Majumder and B. Müller, Electric Charge Separation in Strong Transient Magnetic Fields, Phys. Rev. C 81 (2010) 064912 [arXiv:1003.2436] [SPIRES].
K. Fukushima, M. Ruggieri and R. Gatto, Chiral magnetic effect in the PNJL model, Phys. Rev. D 81 (2010) 114031 [arXiv:1003.0047] [SPIRES].
W.-J. Fu, Y.-L. Wu and Y.-X. 2Liu, Chiral Magnetic Effect and Chiral Phase Transition, Commun. Theor. Phys. 55 (2011) 123 [arXiv:1002.0418] [SPIRES].
S.-i. Nam, Chiral magnetic effect (CME) at low temperature from instanton vacuum, arXiv:0912.1933 [SPIRES].
D.E. Kharzeev, Topologically induced local P and CP-violation in QCD x QED, Annals Phys. 325 (2010) 205 [arXiv:0911.3715] [SPIRES].
D.K. Hong, Anomalous currents in dense matter under a magnetic field, arXiv:1010.3923 [SPIRES].
K. Fukushima and M. Ruggieri, Dielectric correction to the Chiral Magnetic Effect, Phys. Rev. D 82 (2010) 054001 [arXiv:1004.2769] [SPIRES].
P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [SPIRES].
M. Abramczyk, T. Blum, G. Petropoulos and R. Zhou, Chiral magnetic effect in 2+1 flavor QCD+QED, PoS(LAT2009)181 [arXiv:0911.1348] [SPIRES].
P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical study of chiral magnetic effect in quenched SU(2) lattice gauge theory, PoS(LAT2009)080 [arXiv:0910.4682] [SPIRES].
D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [SPIRES].
A. Rebhan, A. Schmitt and S.A. Stricker, Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model, JHEP 01 (2010) 026 [arXiv:0909.4782] [SPIRES].
H.-U. Yee, Holographic Chiral Magnetic Conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [SPIRES].
A. Rebhan, A. Schmitt and S. Stricker, Holographic chiral currents in a magnetic field, Prog. Theor. Phys. Suppl. 186 (2010) 463 [arXiv:1007.2494] [SPIRES].
A. Gorsky, P.N. Kopnin and A.V. Zayakin, On the Chiral Magnetic Effect in Soft-Wall AdS/QCD, Phys. Rev. D 83 (2011) 014023 [arXiv:1003.2293] [SPIRES].
A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic Anomalous Conductivities and the Chiral Magnetic Effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [SPIRES].
V.A. Rubakov, On chiral magnetic effect and holography, arXiv:1005.1888 [SPIRES].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].
N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [SPIRES].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [SPIRES].
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] [SPIRES].
B. Keren-Zur and Y. Oz, Hydrodynamics and the Detection of the QCD Axial Anomaly in Heavy Ion Collisions, JHEP 06 (2010) 006 [arXiv:1002.0804] [SPIRES].
A.V. Sadofyev and M.V. Isachenkov, The chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [SPIRES].
M. Torabian and H.-U. Yee, Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries, JHEP 08 (2009) 020 [arXiv:0903.4894] [SPIRES].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [SPIRES].
T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, arXiv:1102.4334 [SPIRES].
N.P. Landsman and C.G. van Weert, Real and Imaginary Time Field Theory at Finite Temperature and Density, Phys. Rept. 145 (1987) 141 [SPIRES].
T.S. Evans, The Condensed Matter Limit of Relativistic QFT, hep-ph/9510298 [SPIRES].
J.B. Kogut, M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot and A. Zhitnitsky, QCD-like theories at finite baryon density, Nucl. Phys. B 582 (2000) 477 [hep-ph/0001171] [SPIRES].
Y. Matsuo, S.-J. Sin, S. Takeuchi and T. Tsukioka, Magnetic conductivity and Chern-Simons Term in Holographic Hydrodynamics of Charged AdS Black Hole, JHEP 04 (2010) 071 [arXiv:0910.3722] [SPIRES].
B. Sahoo and H.-U. Yee, Holographic chiral shear waves from anomaly, Phys. Lett. B 689 (2010) 206 [arXiv:0910.5915] [SPIRES].
K. Landsteiner, E. Megias and F. Pena-Benitez, work in progress.
J.M. Luttinger, Theory of Thermal Transport Coefficients, Phys. Rev. 135 (1964) A1505.
A.V. Sadofyev, V.I. Shevchenko and V.I. Zakharov, Notes on chiral hydrodynamics within effective theory approach, arXiv:1012.1958 [SPIRES].
B. Mashhoon, Gravitoelectromagnetism: A Brief Review, gr-qc/0311030 [SPIRES].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES].
I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of Holographic Superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [SPIRES].
M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [SPIRES].
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Amado, I., Landsteiner, K. & Pena-Benitez, F. Anomalous transport coefficients from Kubo formulas in Holography. J. High Energ. Phys. 2011, 81 (2011). https://doi.org/10.1007/JHEP05(2011)081
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DOI: https://doi.org/10.1007/JHEP05(2011)081