Related papers: Nahm Transformation on the Lattice
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles…
By exploiting the relation between static zero modes of massless Dirac operator and Kustaanheimo-Stiefel (Hopf) bundle sections, a general zero modes Ansatz which depends on an arbitrary real vector-function on $R^3$ is constructed.
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spectral data: a Hirzebruch surface Z together with a coherent…
We have performed a systematic study of the phase transition in the pure compact U(1) lattice gauge theory in the extended coupling parameter space (\beta, \gamma) on toroidal and spherical lattices. The observation of a non-zero latent…
The fermion determinant and the chiral anomaly of lattice Dirac operator D on a finite lattice are investigated. The condition for D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is…
We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of…
We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite…
A practical implementation of the Overlap-Dirac operator ${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits the sparseness of $H$ and does not require full storage. A simple application to parity invariant three…
The zero modes of the Dirac operator in the background of center vortex gauge field configurations in $\R^2$ and $\R^4$ are examined. If the net flux in D=2 is larger than 1 we obtain normalizable zero modes which are mainly localized at…
We examine the problem of gauge-field localization in higher-dimensional gauge theories. In particular, we study a five-dimensional U(1) by lattice techniques and we find that gauge fields can indeed be localized. Two models are considered.…
The finite temperature transition of QCD can be seen as a change in the structure of the hadrons and as a symmetry breaking transition -- a change in the structure of the vacuum. These phenomena are observed differently and carry…
We demonstrate that certain gauge fixing functionals cannot be added to the action on backgrounds such as de Sitter in which a linearization instability is present. We also construct the field dependent gauge transformation which carries…
A recently proposed method for regularizing chiral gauge theories non-perturbatively is discussed in detail. The result is an effective action which can be computed from the lattice gauge field, and which is suited for numerical…
Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and…
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…
We propose a lattice action including unphysical Wilson fermions with a negative mass m_0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0) cannot appear and…
Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions…
The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as…