Related papers: Generalized Ginsparg-Wilson relations
We study chiral symmetries of fermionic non commutative dipole theories. By using Fujikawa's approach we obtain explicit expressions of the anomalies for Dirac and chiral fermions in 2 and 4 dimensions.
In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show…
I implement a set of tricks for constructing lattice fermion actions which approximately realize the Ginsparg-Wilson relation, with very promising results from simulations.
We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted…
We show that it is possible to improve the chiral behaviour and the approach to the continuum limit of correlation functions in lattice QCD with Wilson fermions by taking arithmetic averages of correlators computed in theories regularized…
This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge…
We analyse stability of almost massless Dirac mode in gauge models with boundary (domain wall) fermions, and consider the possibility of decoupling one of its chiral component by giving it a Majorana mass of the order of the inverse lattice…
We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological…
We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a {\it twisted} formulation of the underlying supersymmetric theory in which the fermions are represented as grassmann valued…
We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for $d=2,3,4,8,9$ mod 8, independently of the signature. These objects permit a…
The general formalism of the free Dirac fermions on spatially flat $(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes is developed in momentum representation. The mode expansions in terms of the fundamental spinors…
We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around…
It is shown that the conflict between lattice chiral symmetry and the Majorana condition in the presence of Yukawa couplings, which was noted in our previous paper, is related in an essential way to the basic properties of Ginsparg-Wilson…
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
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…
In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In $8n$ and $1+8n$ dimensions, we find a difficulty to…
Ginsparg-Wilson relation and admissibility condition have the key role to construct lattice chiral gauge theories. They are also useful to define the chiral structure in finite noncommutative geometries or matrix models. We discuss their…
The Dirac-like equation governing dynamics of free anomalous fermions is derived. The basis bispinors controlling the obtained solutions of this equation turn out to be normalized by the area confining a region in the bispinor Clifford…
Clifford algebras and Majorana conditions are analyzed in any spacetime. An index labeling inequivalent $\Gamma$-structures up to orthogonal conjugations is introduced. Inequivalent charge-operators in even-dimensions, invariant under Wick…