Magnetohydrodynamics
September 2018
Magnetohydrodynamics, or MHD for short, concerns itself with the study of conducting fluids in the presence of strong magnetic fields. See Wikipedia. It describes the coupling of hydrodynamics to Maxwell's electromagnetism. The absence of magnetic monopoles in our universe implies that the magnetic field lines are always closed. This results in a kind of conservation principle stating that, unless influenced by external sources, magnetic field lines can neither be created nor be destroyed. This symmetry is present in any theory of electromagnetism, in particular, MHD.
This symmetry enjoyed by MHD is an example of the so-called higher-form symmetries or generalised symmetries. Unlike ordinary symmetries, where the charged objects are point-like particles like electrons, objects charged under higher-form symmetries are higher-dimensional structures like strings or surfaces. One of my recent projects involved a generic study of hydrodynamics in the presence of such higher-form symmetries [arXiv:1803.00991]. MHD itself is an example of such hydrodynamics with a spontaneously broken one-form symmetry [arXiv:1808.01939], commonly known as string fluids.