Generalized global symmetries and dissipative magnetohydrodynamics

Sašo Grozdanov, Diego M. Hofman, and Nabil Iqbal
Phys. Rev. D 95, 096003 – Published 5 May 2017

Abstract

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.

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  • Received 2 January 2017

DOI:https://doi.org/10.1103/PhysRevD.95.096003

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsParticles & FieldsPlasma Physics

Authors & Affiliations

Sašo Grozdanov1,*, Diego M. Hofman2,†, and Nabil Iqbal2,‡

  • 1Instituut-Lorentz for Theoretical Physics, Leiden University, Niels Bohrweg 2, Leiden 2333 CA, Netherlands
  • 2Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, Netherlands

  • *grozdanov@lorentz.leidenuniv.nl
  • d.m.hofman@uva.nl
  • n.iqbal@uva.nl

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Issue

Vol. 95, Iss. 9 — 1 May 2017

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