Related papers: Weyl and ghost fermions on the lattice
We demonstrate that in the topologically trivial gauge sector the Ginsparg-Wilson relation for lattice Dirac operators admits an exactly gauge invariant path integral formulation of the Weyl fermions on a lattice.
In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here we show that in solid state systems this classification is incomplete and find several additional types of crystal symmetry-protected…
This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity…
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear…
Recently, two solutions have been proposed to the long standing problem of $\mathcal{CP}$-symmetry on the lattice, which is particularly evident when considering the construction of chiral gauge theories. The first, based on a lattice…
We define and study a three dimensional lattice model which displays a Weyl semi-metallic phase. This model consists of coupled layers of quantum (anomalous) Hall insulators. The Weyl semi-metallic phase appears between a resulting quantum…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
We construct Hamiltonian models on a 3+1d cubic lattice for a single Weyl fermion and for a single Weyl doublet protected by exact (as opposed to emergent) chiral symmetries. In the former, we find a not-on-site, non-compact chiral symmetry…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
The construction of massless Majorana fermions with chiral Yukawa couplings on the lattice is considered. We find topological obstructions tightly linked to those underlying the Nielsen-Ninomiya no-go theorem. In contradistinction to chiral…
The Ginsparg-Wilson relation, if written in a suitable form, can be used as a condition for lattice Dirac operators of massless fermions also in odd dimensions. The fermion action with such a Dirac operator is invariant under a generalized…
Witten's anomaly for SU(2) with a single I=1/2 Weyl fermion in four dimension is shown to be reproduced by the lattice overlap. The mechanism is based on Berry's phase, and on the analyticity of the matrix $H$ by which the overlap is…
It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in even number of dimensions that: (a) is ultralocal, (b) respects the symmetries of hypercubic lattice, (c) chirally…
Weyl nodes in three-dimensional Weyl semimetals break the Liouville equation, leading to the Liouville anomaly. Here we present a new approach to derive the semiclassical action and equations of motion for Weyl fermions in the presence of…
We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second…
We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the…
Supersymmetry, like Poincare symmetry, is softly broken at finite lattice spacing provided the gaugino mass term is strongly suppressed. Domain wall fermions provide the mechanism for suppressing this term by approximately imposing chiral…
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of $N=2$ lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious chiral fermion…
This note is a comment on some recent papers that have raised a controversy about the existence of the odd-parity trace anomaly in a four-dimensional theory of Weyl fermions. Without going into too technical details we explain why the…
A new approach to formulate the fermion field on lattice is introduced by proposing a new Dirac operator on lattice.This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation…