We recently performed a pilot study determining the parameters of the leading order chiral La-grangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. We complement a quick survey of our recent preprint [1] by addressing some points raised during discussions at the conference.

The low energy eigenmodes of the continuum QCD Dirac operator are extended, but on the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes. These nonphysical modes can introduce strong lattice artifacts for observables that are sensitive to chiral symmetry, especially in mixed action simulations. We study how these lattice artifacts depend on the parameters ...

We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular we analyze the overlap Dirac operator, a chirally improved Dirac operator and the standard Wilson operator. We discuss the flow of real eigenvalues as a function of the instanton size. An analysis of the eigenvectors shows that, due to their...

We simulate Quantum Chromodynamics (QCD) in four Euclidean dimensions with two (degenerate mass) flavors of dynamical quarks. The Dirac operator we use is the so-called chirally improved Dirac operator. We discuss the algorithm used for the simulation as well as the checks and some results on lattices up to size 8 for fermion mass parameters down to 0.1. This is the first attempt to introduce d...

the degree of φ : S → SU(N), where S is the 3sphere “at infinity” in R. The topological charge has a fermionic description: by the Index Theorem, Q = index(%∂ ) where %∂ A is the Dirac operator coupled to A. The situation is similar for gauge fields on compact manifolds such as S, T , . . . Consider now a family A of SU(N) gauge fields on the 4-torus T 4 parameterized by y ∈ Y (a smooth paramet...

Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...

We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension l...

We consider the Dirac operator D of a Lorentzian spin manifold of even dimension n 4. We prove, that the square D 2 of the Dirac operator on plane wave manifolds and the shifted operator D 2 ? K on Lorentzian space forms of constant sectional curvature K are of Huygens type. Furthermore, we study the Huygens property for coupled Dirac operators on 4-dimensional Lorentzian spin manifolds.

We discuss the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the GinspargWilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ5(1−aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Go...

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...