Emergent gauge symmetries: making symmetry as well as breaking it

Gauge symmetries play an essential role in determining the interactions of particle physics. Where do they come from? Might the gauge symmetries of the Standard Model unify in the ultraviolet or might they be emergent in the infrared, below some large scale close to the Planck scale? Emergent gauge symmetries are important in quantum many-body systems in quantum phases associated with long range entanglement and topological order, e.g. they arise in high temperature superconductors, with string-net condensation and in the A-phase of superfluid 3 He. String-nets and superfluid 3 He exhibit emergent properties similar to the building blocks of particle physics. Emergent gauge symmetries also play an important role in simulations of quantum field theories. This article discusses recent thinking on possible emergent gauge symmetries in particle physics, commenting also on Higgs phenomena and the vacuum energy or cosmological constant puzzle in emergent gauge systems. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Topology of Modal Propositions Depicted by Peirce’s Gamma Graphs: Line, Square, Cube, and Four-Dimensional Polyhedron

This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some (but no all) gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube to the line and the square; and then forwards from the cube to the four-dimensional polyhedron.

Whirling interlayer fields as a new source of stable topological order in moiré CrI3

The moiré engineering of two-dimensional magnets opens unprecedented opportunities to design novel magnetic states via the stacking-dependent magnetism. Here, we explore the formation and control of ground state topological spin structures (TSTs) in moiré CrI3 without including the nearest-neighbor (NN) Dzyaloshinskii-Moriya interactions (DMI) and dipolar interactions in the theoretical approach. Using stochastic Landau-Lifshitz-Gilbert simulations, we unveil the emergence of vortex and antivortex interlayer exchange fields at large moiré periodicity. The whirling fields stabilize spontaneous and field-assisted ground state TSTs with various topologies, including skyrmionic clusters with high topological charges. Furthermore, by examining the effect of the Kitaev interaction and the next NN DMI, we propose the latter as the unique spin-orbit coupling mechanism compatible with the experimental results on monolayer and twisted CrI3. Therefore, our study goes beyond the current knowledge about TSTs in moiré magnets, opens exciting opportunities for moiré skyrmionics, and uncovers the spin-orbit coupling in CrI3.