Related papers: Logarithmic corrections to $\mathbf{a^2}$ scaling …
We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting the discussion to contributions from…
We compute logarithmic corrections to the O(a^2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form $a^2[\ln(a^2)]^{(n/(n-2))}$. We also…
We derive the asymptotic lattice spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ relevant for spectral quantities of lattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson quarks. We give some examples for…
We study anomalous dimensions of (super)conformal Wilson operators at weak and strong coupling making use of the integrability symmetry on both sides of the gauge/string correspondence and elucidate the origin of their single-logarithmic…
We explore the phase diagram of the SU(2) Yang-Mills theory in 5 dimensions by numerical simulations. The lattice system shows a dimensionally-reduced phase where the extra dimension is small compared to the four dimensional correlation…
Lattice artifacts in the 2d O(n) non-linear sigma-model are expected to be of the form O(a^2), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff…
The relativistic corrections to the static potential, i.e. the O(1/m) correction, the O(1/m^2) spin-dependent and momentum-dependent corrections are investigated in SU(3) lattice gauge theory. These corrections are relevant ingredients of…
As a computationally less costly test case for full QCD, we investigate an SU(3) Yang-Mills theory coupled to a bosonic spinor field. This theory corresponds to QCD with minus two quark flavors and is known as the bermion model. Our central…
Maximally supersymmetric Yang--Mills theory (N=4 SYM) is conformal for any value of the coupling. Lattice regularization breaks conformality through the introduction of a non-zero lattice spacing and a finite lattice volume. This…
Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice…
The large $N$ limit of SU($N$) gauge theories is well understood in perturbation theory. Also non-perturbative lattice studies have yielded important positive evidence that 't Hooft's predictions are valid. We go far beyond the statistical…
We perform a tree-level O(a) improvement of two-dimensional N=(2,2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is…
The construction of non-Abelian Euclidean Yang-Mills theories in dimension four, as scaling limits of lattice Yang-Mills theories or otherwise, is a central open question of mathematical physics. This paper takes the following small step…
In lattice gauge theories, the gradient flow has been used extensively both, for scale setting and for defining finite volume renormalization schemes for the gauge coupling. Unfortunately, rather large cutoff effects have been observed in…
One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ with…
We derive the asymptotic lattice-spacing dependence $a^2[2b_0\bar{g}^2(1/a)]^{\hat{\gamma}_i}$ relevant for spectral quantities of lattice QCD, when using unrooted Staggered quarks. Without taking any effects from matching into account we…
Discretization effects of lattice QCD are described by Symanzik's effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $\sim a^n [\bar g^2(a^{-1})]^{\hat\gamma_1} \sim…
When analyzed in terms of the Symanzik expansion, lattice correlators of multi-local (gauge-invariant) operators with non-trivial continuum limit exhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects of the type…
In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by…
The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the…