Electric-magnetic Symmetry Research Articles

Non-invertible surface defects in 2+1d QFTs from half spacetime gauging

We study duality defects in 2+1d theories with ℤN0×ℤN1 global symmetry and trivial mixed ’t Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, obtained from a four-dimensional BF theory gauging a ℤNEM electric-magnetic symmetry. Furthermore, we provide explicit examples of such duality defects in U(1) × U(1) gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d N = (2, 0) SCFTs of type AN−1 on various three-manifolds.

Tiered structure and symmetry of the electromagnetic equations

The structure of Maxwell's equations is reproduced for the potentials introducing a second vector potential , in addition to the usual vector potential . These in turn can be described in terms of the so-called potpotentials and the process continued ad infinitum. A unified scheme is expounded, where the relationship between contiguous and alternate tiers is presented. The Heaviside Larmor (HL) symmetry is fulfilled in any one tier. In the presence of matter, the electric–magnetic symmetry is broken by electric monopoles but preserved for the electric and magnetic dipoles. The Hertz potentials will be shown to be the second tier potentials. The obtention of vector solutions from a scalar solution will be shown to be a direct consequence of linear superposition, the HL symmetry and the structure of the electromagnetic equations for all tiers. The Debye potentials provide such solutions for spherical symmetry. The physical reality of the quantities in any one tier is discussed, in particular regarding the question of gauge transformations and physical observables.

Quantum magnetic monopole condensate

Despite decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental and extends to full quantum behavior. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate dual to the charge Cooper pair condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. The monopole supercurrents result in the electric analog of the Meissner effect and lead to linear confinement of the Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons.

Lateral Optical Force due to the Breaking of Electric-Magnetic Symmetry.

Lateral optical forces in a direction perpendicular to light propagation have attracted increasing interest in recent years. Up to now, all lateral forces can be attributed to the symmetry breaking in the lateral directions caused by either the morphology of the scatterer geometry or the optical fields impinging on the scatterer. Here we demonstrate, both numerically and analytically, that when an isotropic scatterer breaks the electric-magnetic symmetry, a new type of anomalous lateral force can be induced along the direction of translational invariance where the illumination striking the scatterer has no propagation, field gradient, or spin density vortex (Belinfante's spin momentum). Our analytical results are rigorous for an arbitrary size scatterer, ensuring the universality of our conclusion. Furthermore, the electric-magnetic symmetry-breaking-induced lateral force is comparable in magnitude to other components of the optical force and reversible in direction for different polarizations of the illuminating light, rendering it capable of practical optical manipulation as well as enriching the understanding of light-matter interaction.

Electric–magnetic symmetry and Noether's theorem

In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric–magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric–magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.

Phase transitions inZNgauge theory and twistedZNtopological phases

We find a series of non-Abelian topological phases that are separated from the deconfined phase of ${Z}_{N}$ gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the ``twisted'' ${Z}_{N}$ states, are described by a recently studied $U(1)\ifmmode\times\else\texttimes\fi{}U(1)\ensuremath{\rtimes}{Z}_{2}$ Chern-Simons (CS) field theory. The $U(1)\ifmmode\times\else\texttimes\fi{}U(1)\ensuremath{\rtimes}{Z}_{2}$ CS theory provides a way of gauging the global ${Z}_{2}$ electric-magnetic symmetry of the Abelian ${Z}_{N}$ phases, yielding the twisted ${Z}_{N}$ states. We introduce a parton construction to describe the Abelian ${Z}_{N}$ phases in terms of integer quantum Hall states, which then allows us to obtain the non-Abelian states from a theory of ${Z}_{2}$ fractionalization. The non-Abelian twisted ${Z}_{N}$ states do not have topologically protected gapless edge modes and, for $N>2$, break time-reversal symmetry.

Duplex symmetry and its relation to the conservation of optical helicity

Helicity is a familiar concept in particle physics and also appears in the physics of fluids and plasmas. In this paper, we present the optical helicity in a form readily applicable to both quantum and classical problems. We examine the relationship between the optical helicity and the more familiar optical spin and show that the conservation of helicity is an expression of the electric-magnetic symmetry for light. We show that helicity is distinct from Lipkin's 00-zilch; a simple relationship exists between the two only for monochromatic fields. It is only the optical helicity that has the correct dimensions of an angular momentum, thereby accurately describing the helicity of light. To illustrate the physical significance of the optical helicity, we consider a circularly polarized plane wave and the field emitted by a rotating electric dipole.

Towards a non-abelian electric-magnetic symmetry: the skeleton group

We propose an electric-magnetic symmetry group in non-abelian gauge theory, which we call the skeleton group. We work in the context of non-abelian unbroken gauge symmetry, and provide evidence for our proposal by relating the representation theory of the skeleton group to the labelling and fusion rules of charge sectors. We show that the labels of electric, magnetic and dyonic sectors in non-abelian Yang-Mills theory can be interpreted in terms of irreducible representations of the skeleton group. Decomposing tensor products of these representations thus gives a set of fusion rules which contain information about the full fusion rules of these charge sectors. We demonstrate consistency of the skeleton’s fusion rules with the known fusion rules of the purely electric and purely magnetic magnetic sectors, and extract new predictions for the fusion rules of dyonic sectors in particular cases. We also implement S-duality and show that the fusion rules obtained from the skeleton group commute with S-duality.