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$G_2$-QCD, in which the exceptional Lie group $G_2$ replaces the $SU(3)$ gauge group of QCD, does not suffer from a fermion sign problem. It can therefore be simulated also at comparatively low temperatures and high densities on the…
The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom -- leptonic colour, an analogue of the familiar quark…
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD,…
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point…
We present numerical evidence that supports the theory of quark confinement based on center vortex condensation. We introduce a special gauge ("maximal center gauge") and center projection, suitable for identification of center vortices.…
We construct two-dimensional ${\cal N} = (2, 2)$ supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU($N_c$) color group. These lattice theories…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented…
We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or…
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models…
We study the center symmetry of SU(N) gauge theories with fermions in the two-index representations, by computing the effective potential of the Polyakov loop in the large-mass expansion on the lattice. In the large-N limit and at non-zero…
This talk summarizes the results of the DESY-M\"unster collaboration for $\mathcal{N}=1$ supersymmetric Yang-Mills theory with the gauge group SU(3). It is an updated status report with respect to our preliminary data presented at the last…
The interplay of deconfinement and chiral symmetry restoration are considered in terms of effective theories. We generalize the earlier model studies by considering fermions in higher representations, and study the finite temperature phase…
In this paper we present a model of confinement based on an analogy with the confinement mechanism of the Schwarzschild solution of general relativity. Using recently discovered exact, Schwarzschild-like solutions of the SU(2)…
We report on a lattice study of two-color QCD with adjoint staggered fermions at high density. We find that the model has no early onset and we report on results for diquark condensation, from simulations with and without a diquark source…
We investigate the chiral properties of SU(2) gauge theory with six flavors, i.e. six light Dirac fermions in the fundamental representations by lattice simulation, and point out that the spontaneous breakdown of chiral symmetry does not…
Because of the problems arising from the fermion unification in the traditional Grand Unified Theory and the mass hierarchy between the 4-dimensional Planck scale and weak scale, we suggest the low energy gauge unification theory with low…
We review a performance of Fock space methods in calculating spectra of a range of supersymmetric models with gauge symmetry. Examples include: a) SU(2) Supersymmetric Yang Mills Quantum Mechanics in four euclidean dimensions, b) Quantum…
We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are…
We confront the finite volume and small quark mass behaviour of the scalar condensate, determined numerically in quenched lattice QCD using Neuberger fermions, with predictions of quenched chiral perturbation theory. We find that quenched…
We present a general review about the N=1 supersymmetric SU(Nc) Yang-Mills on the lattice focusing our attention on the quenched approximation in supersymmetry. Finally we analyse and discuss the recent results obtained at strong coupling…