Generalised symmetries

Papers

• Resistive relativistic magnetohydrodynamics without Ampère’s law

  R. Lier, A. Jain, J. Armas, O. Porth

  Jan 2025 PRD 2501.04638 INSPIRE Cite

  Magnetic reconnection, where magnetic field lines in a plasma break and rejoin, powers flares and particle acceleration in high-energy astrophysics. It relies on the plasma’s small electrical resistance, which is hard to simulate: in the traditional description, Ampère’s law makes the equations “stiff” and forces tiny time steps. We drop Ampère’s law altogether, using a formulation of magnetohydrodynamics based on a higher-form symmetry in which resistivity acts like a magnetic viscosity, and build a causal numerical scheme that handles strong shocks moving near the speed of light.

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• Higher-group global symmetry and the bosonic M5 brane

  J. Armas, G. Batzios, A. Jain

  Feb 2024 JHEP 2402.19458 INSPIRE Cite

  Physicists classify phases of matter, such as magnets or superfluids, by which symmetries they break. The idea now extends to “higher-form” symmetries, whose charges are extended objects such as strings and membranes, and to “higher groups” that intertwine several of them. We show that such symmetries arise in supergravity, the low-energy limit of string and M-theory, when branes are present, and classify the phases they allow. For the bosonic M5-brane, a five-dimensional object in M-theory, all the fields living on it turn out to be ripples of broken symmetries, called Goldstone modes.

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• Approximate higher-form symmetries, topological defects, and dynamical phase transitions

  J. Armas, A. Jain

  Jan 2023 PRD 2301.09628 INSPIRE Cite

  Higher-form symmetries, whose charges are extended objects such as magnetic field lines, help classify phases of matter. In real materials they are rarely exact: topological defects, such as vortices or charges on which field lines end, break them slightly. We build effective theories and hydrodynamics for such approximate higher-form symmetries and the ways they can be broken. The framework captures phase transitions driven by a proliferation of defects, from the melting of liquid crystals and the ionisation of a gas into a plasma to spin ice and the Meissner effect in superconductors.

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• One-form superfluids & magnetohydrodynamics

  J. Armas, A. Jain

  Nov 2018 JHEP 1811.04913 INSPIRE Cite

  Magnetohydrodynamics, the theory of electrically conducting plasmas, describes everything from accretion disks around black holes to fusion reactors. We reformulate it using generalised symmetries, in which the fact that magnetic field lines never end becomes a symmetry, and show that magnetohydrodynamics is a “one-form superfluid” in which this symmetry is partly broken. Breaking it completely describes plasmas without free charges that can still be polarised, such as a neutral gas bathed in light, for which we build the first hydrodynamic theory. We also map out their equilibrium states.

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• Magnetohydrodynamics as superfluidity

  J. Armas, A. Jain

  Aug 2018 PRL 1808.01939 INSPIRE Cite

  Magnetohydrodynamics describes how plasmas and magnetic fields move together, in stars and galaxies as well as in fusion experiments. We show that it can be recast as a new kind of superfluid. Magnetic field lines never end, since there are no magnetic monopoles, and this can be viewed as a “one-form” symmetry; in a plasma the symmetry is spontaneously broken, with a magnetic scalar potential as its Goldstone mode. This writes magnetohydrodynamics purely as conservation equations, better suited to simulations, and settles how its equilibrium states should be defined.

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• Dissipative hydrodynamics with higher-form symmetry

  J. Armas, J. Gath, A. Jain, A. V. Pedersen

  Mar 2018 JHEP 1803.00991 INSPIRE Cite

  In ordinary fluids, conserved quantities are carried by particles. In some systems they are carried by extended objects such as strings or membranes; in a plasma, magnetic field lines behave like conserved strings. We build the theory of dissipative fluids filled with such objects, which flow differently along and across them, and identify all the transport coefficients, such as viscosities and resistivities, that characterise them at leading order. We also describe interfaces between phases of such fluids, where ripples on the surface show clear signs of the fluid’s directionality.

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Talks