^{1,2}

^{,*}

^{3}

^{,†}

^{3}.

We show that relativistic magnetohydrodynamics (MHD) can be recast as a novel theory of superfluidity. This new theory formulates MHD just in terms of conservation equations, including dissipative effects, by introducing appropriate variables such as a magnetic scalar potential, and providing necessary and sufficient conditions to obtain equilibrium configurations. We show that this scalar potential can be interpreted as a Goldstone mode originating from the spontaneous breaking of a one-form symmetry, and present the most generic constitutive relations at one derivative order for a parity-preserving plasma in this new superfluid formulation.

Relativistic magnetohydrodynamics (MHD) provides a universal framework to study plasma physics in astrophysical settings as well as in laboratory experiments

Traditional treatments of MHD are formulated in terms of a stress tensor

In practice, however, for instance in numerical approaches, Maxwell’s equations can be used to eliminate

Extrapolating this line of thought, the authors of Ref.

If we switch off the sources

As pointed out in Ref.

Finally, while the traditional and string fluid formulations of MHD can easily be shown to be equivalent at ideal order as described above, at higher derivative orders this equivalence is quite nontrivial. It has only been established in the dissipative sector for linear fluctuations (Kubo formulas) in a state with

Hydrodynamics is the study of small fluctuations of a quantum system around thermodynamic equilibrium and hence it is important to understand how to describe equilibrium configurations. As usual, one assumes the existence of an arbitrary time coordinate

These considerations lead us to reevaluate whether the string fluid variables

In order to construct a gauge-invariant vector, we need to introduce a scalar field

The transformation of

The dynamics of one-form superfluids is also governed by Eq.

In order to discuss the constitutive relations of a one-form superfluid in four spacetime dimensions, we decompose

Restring ourselves to derivative corrections that respect

The hydrostatic sector of the theory has not been considered in Refs.

As an example, we consider the first order charge current

Note that the equivalence between the two formulations, even just in the dissipative sector, required the presence of the hydrostatic coefficient

This description of MHD as superfluidity is entirely based on conservation equations, even when including dissipation effects. Together with the understanding of the necessary conditions for equilibrium, it can provide initial configurations for obtaining interesting insights in the context of astrophysical phenomena using numerical simulations (e.g., Ref.

We would like to thank J. Bhattacharya, J. Hernandez, and specially N. Iqbal for various helpful discussions. We would also like to thank J. Bhattacharya, S. Grozdanov, and N. Iqbal for comments on an earlier draft. J. A. is partly supported by the Netherlands Organization for Scientific Research (NWO). A. J. would like to thank the Perimeter Institute, where part of this project was done, for hospitality. A. J. is supported by the Durham Doctoral Scholarship offered by Durham University.

Parity

In making these identifications, we have assumed

The authors of Ref.