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Following a recent proposal by Cooper and Zwanziger we investigate via $SU(2)$ lattice simulations the effect on the Coulomb gauge propagators and on the Gribov-Zwanziger confinement mechanism of selecting the Gribov copy with the smallest non-trivial eigenvalue of the Faddeev-Popov operator, i.e.~the one closest to the Gribov horizon. Although such choice of gauge drives the ghost propagator towards the prediction of continuum calculations, we find that it actually overshoots the goal. With increasing computer time, we observe that Gribov copies with arbitrarily small eigenvalues can be found. For such a method to work one would therefore need further restrictions on the gauge condition to isolate the physically relevant copies, since e.g.~the Coulomb potential $V_C$ defined through the Faddeev-Popov operator becomes otherwise physically meaningless. Interestingly, the Coulomb potential alternatively defined through temporal link correlators is only marginally affected by the smallness of the eigenvalues., Comment: 11 pages, 13 figures. Discussion and conclusions extended, some plots changed. To appear in PRD

We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter., Comment: 32 pages, 15 figures. Typos corrected; to appear on PRD

Our previous studies of Coulomb gauge Yang-Mills theory are extended to finite temperature. We investigate the SU(2) static gluon and ghost propagators and show results for the Coulomb potential, with a focus on the Gribov ambiguity. To compute these quantities at high temperatures and to solve scaling violations we use the anisotropic Wilson gauge action., Comment: 7 pages, 4 figures. Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4, concentrating on the stability of 't Hooft loops. High precision calculations have been performed in D=3; similar results hold also for D=4 and D=2. We discuss the impact of our findings on the continuum limit of Yang-Mills theories., Comment: 7 pages, 3 figures. Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be derived using unitary transformations to take care of time evolution. Alternatively, the exact solution can also be found in Coulomb gauge using the exact ground state wave functional which is known explicitly in these simple cases. The Coulomb gauge technique can also be applied to the more realistic case of Yang-Mills theory in (3+1) dimensions, where one has to rely on the approximate vacuum wave functional obtained e.g. in recent variational approaches. We use this formulation to compute the temporal Wilson loop in (3+1) dimensional Yang-Mills theory, and find that the Wilson and Coulomb string tension agree within this approximation scheme. Possible improvements of these findings are briefly discussed., Comment: 8 pages; uses PoS.cls; talk given by M. Quandt at "Quark Confinement and the Hadron Spectrum X", Munich, Germany, Oct. 8-12, 2012

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed., Comment: 24 pages, 4 eps-figures; new version matches published one

We study the continuum limit of adjoint SU(2) LGT by means of a suppression term for Z2 monopoles. High barriers for tunnelling among different twist sectors are overcome through parallel tempering. Monopole condensation is used to study the deconfinement transition and the properties of the confined phase. Ergodicity in summing over all twist sectors allows an unbiased measure of the 't Hooft vortices free energy. Its behaviour in the SO(3) confined phase hints at differences from what conjectured for semi-integer discretizations., Comment: Contribution to LATTICE 05, Dublin.

We present preliminary results for a non perturbative determination of the parameters in the action required to restore Lorentz invariance in long distance correlators, using the static interquark potential. Comparison with analytical results is made and further applications are discussed., Comment: 3 pages, Lattice2003 (improvement)

A generalization of anisotropic lattices to include a 2+2 discretization is discussed. As a part of this program, we determine the one-loop correction to the gluon self-energy and analyse the restoration of Lorentz invariance in on-shell states for both the 2+2 and 3+1 cases. A 2+2 Wilson-like fermion action is also considered., Comment: 3 pages, Lattice2003(improve)

The implementation of gauge theories on a four-dimensional anisotropic lattice with two distinct lattice spacings is discussed, with special attention to the case where two axes are finely and two axes are coarsely discretized. Feynman rules for the Wilson gauge action are derived and the renormalizability of the theory and the recovery of the continuum limit are analyzed. The calculation of the gluon propagator and the restoration of Lorentz invariance in on-shell states is presented to one-loop order in lattice perturbation theory for $SU(N_c)$ on both 2+2 and 3+1 lattices., Comment: 27 pages, uses feynmf. Font compatibility adjusted

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of L\" uscher and Weisz to higher-loop integrals with fermions., Comment: Talk presented at LATTICE96(theoretical developments) Postscript file avalaible at http://www1.le.infn.it:8080/~caraccio/TCMS.html

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of L\"{u}scher and Weisz to higher-loop integrals with fermions., Comment: Postscript file avalaible at http://www1.le.infn.it:8080/~caraccio/TCMS.html