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Generalized global symmetries and dissipative magnetohydrodynamics

Grozdanov, Sašo; Hofman, Diego M.; Iqbal, Nabil

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Sašo Grozdanov

Diego M. Hofman


The conserved magnetic flux of U(1) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are seven dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfvén modes. Finally, we demonstrate that a nontrivial truncation of the theory can be performed at low temperatures compared to the magnetic field: this theory has an emergent Lorentz invariance along magnetic field lines, and hydrodynamic fluctuations are now parametrized by a fluid tensor rather than a fluid velocity. Throughout, no assumption is made of weak electromagnetic coupling. Thus, our theory may have phenomenological relevance for dense electromagnetic plasmas.


Grozdanov, S., Hofman, D. M., & Iqbal, N. (2017). Generalized global symmetries and dissipative magnetohydrodynamics. Physical Review D, 95(9), Article 096003.

Journal Article Type Article
Acceptance Date Jan 2, 2017
Online Publication Date May 5, 2017
Publication Date May 5, 2017
Deposit Date May 8, 2017
Publicly Available Date May 9, 2017
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 95
Issue 9
Article Number 096003
Related Public URLs


Accepted Journal Article (641 Kb)

Copyright Statement
Reprinted with permission from the American Physical Society: Physical Review D 95, 096003 © 2017 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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