Related papers: Ginsparg-Wilson relation on a fuzzy 2-sphere for a…
Gauge theories with fermions in adjoint and fundamental representations are relevant for many different applications including composite Higgs models and general aspects of the confinement problem. We present first results from simulations…
It was shown recently by I. Horvath that lattice fermions obeying the standard form of the Ginsparg-Wilson relation cannot be ultralocal. However, there are more general forms of the Ginsparg-Wilson relation, which also guarantee the…
We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of…
In the framework of perturbation theory, it is possible to put chiral gauge theories on the lattice without violating the gauge symmetry or other fundamental principles, provided the fermion representation of the gauge group is…
During the last several years a non-perturbative formulation of exact chiral symmetry on the lattice has been developed. I shall outline the main ideas of these developments and discuss prospects for the future. The focus will be on the…
The axial anomaly equation in 1+1 dimensional QED is obtained on the lattice for fermions obeying the Ginsparg-Wilson relation. We make use of the properties of the Lattice Dirac sea to investigate the connection between the anomaly and the…
A Ginsparg-Wilson Relation (GWR) is obtained in the presence of chiral symmetry breaking terms. It leads to the PCAC relation as well as an anomaly relation on the lattice. For general fermions, the deviation from the exact GWR is getting…
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their…
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion.…
The Baxter 8-vertex model is equivalent to a particular lattice formulation of a self-interacting, massive Dirac fermion theory. In the time-continuum limit, the lattice Hamiltonian (XYZ spin chain) can be explicitly transformed to a…
On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion…
I review recent progress in the implementation of lattice fermions satisfying the Ginsparg-Wilson relation and some physical applications.
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible…
We study the index of the Ginsparg-Wilson Dirac operator on a noncommutative torus numerically. To do this, we first formulate an admissibility condition which suppresses the fluctuation of gauge fields sufficiently small. Assuming this…
In this letter we show that the overlap formulation of chiral gauge theories correctly reproduces the gravitational Lorentz anomaly in 2-dimensions. This formulation has been recently suggested as a solution to the fermion doubling problem…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented…
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point…
In this article we study field-theoretical aspects of multipolar topological insulators. Previous research has shown that such systems naturally couple to higher-rank tensor gauge fields that arise as a result of gauging dipole or subsystem…
We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural…