Abstract
Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects. We focus on a holographic model which has the same global symmetry as that of low energy plasma and obtain the lifetime of (non-conserved) electric flux in a strong magnetic field regime. The lifetime is inversely correlated to the magnetic field strength and thus suppressed in the strong field regime.
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L.D. Landau and E.M. Lifshitz, Fluid Mechanics, 2nd ed., Butterworth-Heinemann (1987) [DOI].
R.W. Zwanzig, Statistical mechanics of irreversibility, Lectures on Theoretical Physics, Volume 3, Interscience (1961).
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, Perseus Books, (1995).
S.A. Hartnoll and D.M. Hofman, Locally Critical Resistivities from Umklapp Scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
S. Grozdanov, D.M. Hofman and N. Iqbal, Generalized global symmetries and dissipative magnetohydrodynamics, Phys. Rev. D 95 (2017) 096003 [arXiv:1610.07392] [INSPIRE].
D. Schubring, Dissipative String Fluids, Phys. Rev. D 91 (2015) 043518 [arXiv:1412.3135] [INSPIRE].
J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].
J. Armas and A. Jain, Magnetohydrodynamics as superfluidity, Phys. Rev. Lett. 122 (2019) 141603 [arXiv:1808.01939] [INSPIRE].
J. Armas and A. Jain, One-form superfluids & magnetohydrodynamics, JHEP 01 (2020) 041 [arXiv:1811.04913] [INSPIRE].
W.G. Dixon, Special relativity: the foundation of macroscopic physics, Cambridge University Press Archive (1982).
A.M. Anile, Relativistic fluids and magneto-fluids: With applications in astrophysics and plasma physics, Cambridge University Press (2005).
S.S. Komissarov, A Godunov-type scheme for relativistic magnetohydrodynamics, Mon. Not. Roy. Astron. Soc. 303 (1999) 343.
P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results, JHEP 11 (2000) 001 [hep-ph/0010177] [INSPIRE].
J. Pétri, Theory of pulsar magnetosphere and wind, J. Plasma Phys. 82 (2016) 635820502 [arXiv:1608.04895] [INSPIRE].
R.D. Blandford and R.L. Znajek, Electromagnetic extractions of energy from Kerr black holes, Mon. Not. Roy. Astron. Soc. 179 (1977) 433 [INSPIRE].
S.S. Komissarov, Electrodynamics of black hole magnetospheres, Mon. Not. Roy. Astron. Soc. 350 (2004) 407 [astro-ph/0402403] [INSPIRE].
P. Goldreich and W.H. Julian, Pulsar electrodynamics, Astrophys. J. 157 (1969) 869 [INSPIRE].
T. Wiegelmann and T. Sakurai, Solar Force-free Magnetic Fields, Living Rev. Sol. Phys. 9 (2012) 5 [arXiv:1208.4693] [INSPIRE].
S.E. Gralla and T. Jacobson, Spacetime approach to force-free magnetospheres, Mon. Not. Roy. Astron. Soc. 445 (2014) 2500 [arXiv:1401.6159] [INSPIRE].
G. Compère, S.E. Gralla and A. Lupsasca, Force-Free Foliations, Phys. Rev. D 94 (2016) 124012 [arXiv:1606.06727] [INSPIRE].
T. Uchida, Theory of force-free electromagnetic fields. I. general theory, Phys. Rev. E 56 (1997) 2181.
C. Thompson and O. Blaes, Magnetohydrodynamics in the extreme relativistic limit, Phys. Rev. D 57 (1998) 3219 [INSPIRE].
S.E. Gralla and N. Iqbal, Effective Field Theory of Force-Free Electrodynamics, Phys. Rev. D 99 (2019) 105004 [arXiv:1811.07438] [INSPIRE].
P. Glorioso and D.T. Son, Effective field theory of magnetohydrodynamics from generalized global symmetries, arXiv:1811.04879 [INSPIRE].
B. Benenowski and N. Poovuttikul, Classification of magnetohydrodynamic transport at strong magnetic field, arXiv:1911.05554 [INSPIRE].
S. Grozdanov and N. Poovuttikul, Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma, JHEP 04 (2019) 141 [arXiv:1707.04182] [INSPIRE].
D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018) 005 [arXiv:1707.08577] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
J.F. Fuini and L.G. Yaffe, Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field, JHEP 07 (2015) 116 [arXiv:1503.07148] [INSPIRE].
S. Janiszewski and M. Kaminski, Quasinormal modes of magnetic and electric black branes versus far from equilibrium anisotropic fluids, Phys. Rev. D 93 (2016) 025006 [arXiv:1508.06993] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, Phys. Rev. D 99 (2019) 086012 [arXiv:1810.10016] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
C.-F. Chen and A. Lucas, Origin of the Drude peak and of zero sound in probe brane holography, Phys. Lett. B 774 (2017) 569 [arXiv:1709.01520] [INSPIRE].
R.A. Davison, S.A. Gentle and B. Goutéraux, Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states, Phys. Rev. D 100 (2019) 086020 [arXiv:1812.11060] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
R.A. Davison and A. Parnachev, Hydrodynamics of cold holographic matter, JHEP 06 (2013) 100 [arXiv:1303.6334] [INSPIRE].
U. Moitra, S.K. Sake and S.P. Trivedi, Near-Extremal Fluid Mechanics, JHEP 02 (2021) 021 [arXiv:2005.00016] [INSPIRE].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
E. D’Hoker, P. Kraus and A. Shah, RG Flow of Magnetic Brane Correlators, JHEP 04 (2011) 039 [arXiv:1012.5072] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic Field Induced Quantum Criticality via new Asymptotically AdS5 Solutions, Class. Quant. Grav. 27 (2010) 215022 [arXiv:1006.2573] [INSPIRE].
P. Kovtun and A. Starinets, Thermal spectral functions of strongly coupled N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 96 (2006) 131601 [hep-th/0602059] [INSPIRE].
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth dover printing, tenth gpo printing ed., Dover New York (1964).
D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].
P. Glorioso, M. Crossley and H. Liu, A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems, arXiv:1812.08785 [INSPIRE].
J. de Boer, M.P. Heller and N. Pinzani-Fokeeva, Holographic Schwinger-Keldysh effective field theories, JHEP 05 (2019) 188 [arXiv:1812.06093] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, 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].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer New York, (2013).
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Poovuttikul, N., Rajagopal, A. Operator lifetime and the force-free electrodynamic limit of magnetised holographic plasma. J. High Energ. Phys. 2021, 91 (2021). https://doi.org/10.1007/JHEP09(2021)091
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DOI: https://doi.org/10.1007/JHEP09(2021)091