Unstable Modes and Confinement in the Lattice Schr\"odinger Functional Approach

We analyze the problem of the Nielsen-Olesen unstable modes in the SU(2) lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible with the presence of the unstable modes. We put out a possible relation between the dynamics of the unstable modes and the confinement.Comment: 15 pages, LaTeX2e file, 5 figure

Exploring the Dynamics of Three-Dimensional Lattice Gauge Theories by External Fields

We investigate the dynamics of three-dimensional lattice gauge theories by means of an external Abelian magnetic field. For the SU(2) lattice gauge theory we find evidence of the unstable modes.Comment: 3 pages, PostScript. Contribution to the LATTICE 93 Conference (Dallas, U.S.A., September 1993) preprint BARI-TH-162/9

QCD dynamics in a constant chromomagnetic field

We investigate the phase transition in full QCD with two flavors of staggered fermions in presence of a constant abelian chromomagnetic field. We find that the critical temperature depends on the strength of the chromomagnetic field and that the deconfined phase extends to very low temperatures for strong enough fields. As in the case of zero external field, a single transition is detected, within statistical uncertainties, where both deconfinement and chiral symmetry restoration take place. We also find that the chiral condensate increases with the strength of the chromomagnetic field.Comment: 18 pages, 8 figures, 1 tabl

Color Dynamics in External Fields

We investigate the vacuum dynamics of U(1), SU(2), and SU(3) lattice gauge theories in presence of external (chromo)magnetic fields, both in (3+1) and (2+1) dimensions. We find that the critical coupling for the phase transition in compact U(1) gauge theory is independent of the strength of an external magnetic field. On the other hand we find that, both in (3+1) and (2+1) dimensions, the deconfinement temperature for SU(2) and SU(3) gauge systems in a constant abelian chromomagnetic field decreases when the strength of the applied field increases. We conclude that the dependence of the deconfinement temperature on the strength of an external constant chromomagnetic field is a peculiar feature of non abelian gauge theories and could be useful to get insight into color confinement.Comment: 26 pages, 14 figure

Investigations on the deconfining phase transition in QCD

We investigate the deconfining phase transition in SU(3) pure gauge theory and in full QCD with two flavors of staggered fermions by means of a gauge invariant thermal partition functional. In the pure gauge case our finite size scaling analysis is in agreement with the well known weak first order phase transition. In the case of 2 flavors full QCD we find that the phase transition is consistent with weak first order, contrary to the expectation of a crossover for not too large quark masses.Comment: 3 pages, 3 figures, Lattice2003(topology

The phase diagram of QCD with four degenerate quarks

We revisit the determination of the pseudo-critical line of QCD with four degenerate quarks at non-zero temperature and baryon density by the method of analytic continuation. We determine the pseudo-critical couplings at imaginary chemical potentials by high-statistics Monte Carlo simulations and reveal deviations from the simple quadratic dependence on the chemical potential visible in earlier works on the same subject. Finally, we discuss the implications of our findings for the shape of the pseudo-critical line at real chemical potential, comparing different possible extrapolations.Comment: 8 pages, 8 figures, 2 table

Indications on the Higgs boson mass from lattice simulations

The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that the vacuum field and its quantum fluctuations rescale in the same way. The results of the present lattice simulation, confirming previous numerical indications, show that this assumption is not true. As a consequence, large values of the Higgs mass $m_H$ can coexist with the limit $\Lambda\to \infty$. As an example, by extrapolating to the Standard Model our results obtained in the Ising limit of the one-component theory, one can obtain a value as large as $m_H=760 \pm 21$ GeV, independently of $\Lambda$.Comment: 3 pages, 2 figures, Lattice2003(higgs

Probing the non-perturbative dynamics of SU(2) vacuum

The vacuum dynamics of SU(2) lattice gauge theory is studied by means of a gauge-invariant effective action defined using the lattice Schr\"odinger functional. Numerical simulations are performed both at zero and finite temperature. The vacuum is probed using an external constant Abelian chromomagnetic field. The results suggest that at zero temperature the external field is screened in the continuum limit. On the other hand at finite temperature it seems that confinement is restored by increasing the strength of the applied field.Comment: 29 pages, 10 figures, LaTeX2