Related papers: Transiting topological sectors with the overlap
I derive the overlap Dirac operator starting from the overlap formalism, discuss the numerical hurdles in dealing with this operator and present ways to overcome them.
We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors…
Three complementary views on the QCD vacuum structure, all based on eigenmodes of the overlap operator, are reported in their interrelation: (i) spectral density, localization and chiral properties of the modes, (ii) the possibility of…
We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In…
We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of $\cal{N}=$ 4 SYM. We find that the language of code subspaces is…
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
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…
Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap,…
We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying…
Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…
We compute eigenmodes of the lattice Dirac operator for quenched SU(3) gauge configurations on the 4-torus with topological charge 1. We find a strong dependence of the zero modes on the boundary conditions which we impose for the Dirac…
The interplay between between gauge-field winding numbers, theta-vacua, and the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To assess the weight of each topological sector, we compare the mass-dependent chiral…
The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We evaluate first the continuum overlap, which is convergent and well-defined, and yields the correct string…
Gluon field configurations with non-trivial topology like instantons, magnetic monopoles and center vortices play a crucial role in QCD and, in particular, for the spontaneous breaking of chiral symmetry. Moreover, center vortices are…
The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and planar straight-line graphs. For the latter, several variants have been studied (e.g., edge slides and edge…
Overlap formalism deals with the construction of chiral gauge theories on the lattice. These set of lectures provide a pedagogical introduction to the subject with emphasis on chiral anomalies and gauge field topology. Subtleties associated…
For two decades it was believed that chiral symmetries cannot be realized in lattice field theory but this has changed now. Highlights of these new developments will be presented with emphasis on the mathematical structure of the so called…
We give an explicit proof for the locality of staggered overlap operators. The proof covers the original two flavor construction by Adams as well as a single flavor version. As in the case of Neuberger's operator, an admissibility condition…
We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at the…
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…