Abstract
We use the framework of generalised global symmetries to study various hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The latter of these describes a one-form superfluid, which is characterised by a vector Goldstone mode and a two-form superfluid velocity. Two special limits of this theory have been studied in detail: the string fluid limit where the U(1) one-form symmetry is partly restored, and the electric limit in which the symmetry is completely broken. The transport properties of these theories are investigated in depth by studying the constraints arising from the second law of thermodynamics and Onsager’s relations at first order in derivatives. We also construct a hydrostatic effective action for the Goldstone modes in these theories and use it to characterise the space of all equilibrium configurations. To make explicit contact with hot electromagnetism, the traditional treatment of magnetohydrodynamics, where the electromagnetic photon is incorporated as dynamical degrees of freedom, is extended to include parity-violating contributions. We argue that the chemical potential and electric fields are not independently dynamical in magnetohydrodynamics, and illustrate how to eliminate these within the hydrodynamic derivative expansion using Maxwell’s equations. Additionally, a new hydrodynamic theory of non-conducting, but polarised, plasmas is formulated, focusing primarily on the magnetically dominated sector. Finally, it is shown that the different limits of one-form superfluids formulated in terms of generalised global symmetries are exactly equivalent to magnetohydrodynamics and the hydrodynamics of non-conducting plasmas at the non-linear level.
Highlights
Hot electromagnetism is the theory that describes the interaction between electromagnetic and thermal degrees of freedom of matter at finite temperature
It is shown that the different limits of one-form superfluids formulated in terms of generalised global symmetries are exactly equivalent to magnetohydrodynamics and the hydrodynamics of non-conducting plasmas at the non-linear level
We provide a new formulation of dissipative MHD in terms of a system with higher-form conservation laws, which is better suited for numerical studies, classify all dissipative transport coefficients that appear at first order in a long-wavelength expansion and resolve standing issues related to the definition of hydrostatic equilibrium
Summary
Hot electromagnetism is the theory that describes the interaction between electromagnetic and thermal degrees of freedom of matter at finite temperature. The traditional treatment as developed here, following [3], is more general than its corresponding formulation in terms of generalised global symmetries, as it is capable of describing plasmas that are not necessarily electrically neutral at the hydrodynamic length scales.. The traditional treatment of the bound-charge plasma regime is formulated for the first time, and is applicable to non-conducting plasmas (i.e. plasmas with only bound-charges and no free charge carriers) These are argued to be exactly equivalent to one-form superfluids, with the explicit mapping of constitutive relations worked out at ideal order. At first order in derivatives, attention is given to the magnetic dominated bound-charge plasma, where Bμ = O(1) and Eμ = O(∂), to MHD These are shown to be exactly equivalent to the electric limit of one-form superfluids, provided that a certain transport coefficient q× is set to zero. We have formulated an order parameter that describes the partial breaking of the one-form symmetry required to formulate MHD in the language of generalised global symmetries
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
