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We present evidence that seemingly elementary and non-composite objects, namely isolated static fermions in certain gauge Higgs theories, have a mass spectrum corresponding to localized excitations of the surrounding gauge and Higgs fields.

This review article is an exploration of G. Spencer-Brown’s well-known work on the Laws of Form and its relationship to physical science, focusing on correspondence with Majorana fermions.

The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry ‘mixes’ a Killing vector with its fermionic spinor ‘superpartner’ and the Killing equations with the generalization of the Killing spinor equations. The latter reduces to the standard Killing spinor equation, albeit with a fermionic spinor, when the fermionic fields are set to zero. Using these supersymmetry transformations in the spacetime component approach, we construct a Noether-Wald charge of N = 1, D = 4 supergravity with fermionic contributions which is diff-, Lorentz- and supersymmetry-invariant (up to a total derivative). The Killing supervector formalism for the maximal D = 11 supergravity and some related issues are also discussed.

We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasiparticles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drude and phonon peaks at low temperatures, we reveal two intermediate quasilinear interband contributions separated by a kink at 0.2 eV. Using Wannier tightbinding models based on first-principle calculations, we link the optical conductivity above and below 0.2 eV to interband transitions near the double Weyl fermion and a threefold fermion, respectively. We analyze and determine the chemical potential relative to the energy of the threefold fermion, revealing the importance of transitions between a linearly dispersing band and a flat band. More strikingly, below 0.1 eV our data are best explained if spin-orbit coupling is included, suggesting that at these energies, the optical response is governed by transitions between a previously unobserved fourfold spin-3/2 node and a Weyl node. Our comprehensive combined experimental and theoretical study provides a way to resolve different types of multifold fermions in CoSi at different energy. More broadly, our results provide the necessary basis to interpret the burgeoning set of optical and transport experiments in chiral topological semimetals.

A brief overview of the fermionic modes localized on topological solitons is presented.

In this article, we consider charged fermion particle radiation around Kerr – Newman – Vaidya black holes. Using the Hamilton – Jacobi method we derived the emission probability and the temperature of the Hawking radiations. We obtained that the temperature is equal to that due to scalar particles times a factor that contains some characteristics of fermions.

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl 3 , continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin–orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl 3 as a prime candidate for fractionalized Kitaev physics. Inelastic neutron scattering characterization shows that α-RuCl 3 is close to an experimental realization of a Kitaev quantum spin liquid on a honeycomb lattice. The collective excitations provide evidence for deconfined Majorana fermions.

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples like the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

Recent experiments by Gutiérrez et al (2016 Nat. Phys. 12 950) on a graphene-copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice-a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called 'Kek-Y' texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field B, the valley degeneracy of the B-dependent Landau levels is removed by the valley-momentum locking but a B-independent and valley-degenerate zero-mode remains.

We discuss a mixed-action approach in which sea quarks are regularised using non-perturbatively O( a ) improved Wilson fermions, while a fully-twisted tmQCD action is used for valence quarks. In this setup, automatic O( a ) improvement is preserved for valence observables, apart from small residual O( a ) effects from the sea. A strategy for matching sea and valence is set up, and carried out for N f = 2 + 1 CLS ensembles with open boundary conditions at several simulation points. The scaling of basic light-quark observables such as the pseudoscalar meson decay constant is studied, as well as the isospin splitting of pseudoscalar meson masses.