One-form superfluids & magnetohydrodynamics

• Published in: The journal of high energy physics Vol. 2020; no. 1; pp. 1 - 75
• Main Authors: Armas, Jay, Jain, Akash
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020; Springer Nature B.V; SpringerOpen
• Subjects: Chemical potential; Classical and Quantum Gravitation; Computational fluid dynamics; Effective Field Theories; Electric contacts; Electric fields; Electromagnetism; Elementary Particles; Fluid flow; Fluids; Global Symmetries; High energy physics; Holography and quark-gluon plasmas; Magnetohydrodynamics; Organic chemistry; Physics; Physics and Astronomy; Plasmas (physics); Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spontaneous Symmetry Breaking; String Theory; Superfluidity; Symmetry; Thermodynamics; Transport properties; Global Symmetries; Effective Field Theories; Spontaneous Symmetry Breaking; Holography and quark-gluon plasmas
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2020)041

A bstract 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.