What we do understand of Colour Confinement

A review is presented of what we understand of colour confinement in QCD. Lattice formulation provides evidence that QCD vacuum is a dual superconductor: the chromoelectric field of a $q\bar q$ pair is constrained by dual Meissner effect into a dual Abrikosov flux tube and the static potential energy is proportional to the distance.Comment: 10 pages, 5 figures, plenary talk at "Quark Matter 99", Torino, Italy, May 10-15, 199

Topology in QCD with 4 flavours of dynamical fermions

We study the topological properties of full QCD with four flavours of dynamical staggered fermions. In particular the topological susceptibility is measured and the problem of the determination of its first derivative is discussed.Comment: LATTICE99(Topology and Confinement). 3 pages, contains espcrc2.sty fil

Topological susceptibility at zero and finite TT in SU(3) Yang-Mills theory

We determine the topological susceptibility $\chi$ at T=0 in pure SU(3) gauge theory and its behaviour at finite $T$ across the deconfining transition. We use an improved topological charge density operator. $\chi$ drops sharply by one order of magnitude at the deconfining temperature $T_c$.Comment: Recently appeared erratum added as an "Appendix" to the original pape

Topological properties of QCD with two dynamical fermions

We investigate the topological susceptibility of the QCD vacuum with two flavours of dynamical staggered fermions on the lattice both at zero and finite temperature. At zero temperature we study the dependence of the signal on the fermion mass and at finite temperature we analyze the behaviour across the phase transition.Comment: LATTICE99(finite temperature and density). 3 pages, contains espcrc2.sty fil

A disorder analysis of the Ising model

Lattice studies of monopole condensation in QCD are based on the construction of a disorder parameter, a creation operator of monopoles which is written in terms of the gauge fields. This procedure is expected to work for any system which presents duality. We check it on the Ising model in 2d, which is exactly solvable. The output is an amusing exercise in statistical mechanics.Comment: 14 pages, 3 figure

Colour confinement and dual superconductivity of the vacuum - I

We study dual superconductivity of the ground state of SU(2) gauge theory, in connection with confinement. We do that measuring on the lattice a disorder parameter describing condensation of monopoles. Confinement appears as a transition to dual superconductor, independent of the abelian projection defining monopoles. Some speculations are made on the existence of a more appropriate disorder parameter. A similar study for SU(3) is presented in a companion paper.Comment: Some typos corrected, acknowledgements added; to appear on Phys. Rev.

Dual Superconductivity and Chiral Symmetry in Full QCD

A disorder parameter detecting dual superconductivity of the vacuum is measured across the chiral phase transition in full QCD with two flavours of dynamical staggered fermions. The observed behaviour is similar to the quenched case.Comment: Lattice2001(confinement) proceedings, 3 pages, 2 eps figure

A New Custodian for a Realistic Higgsless Model

We present an example of a realistic Higgsless model that makes use of alternative $SU(2)_R$ assignments for the top and bottom quarks recently proposed by Agashe et al. which results in an enhanced custodial symmetry. Using these new representat ions reduces the deviations in the $Zb_\ell\bar{b}_\ell$ coupling to $\sim 4$ for a wide range of parameters, while this remaining correction can also be eliminated by varying the localization parameter (bulk mass) for $b_r$.Comment: 11 pages, 2 figure

Magnetic charge superselection in the deconfined phase of Yang-Mills theory

The vacuum expectation value of an operator carrying magnetic charge is studied numerically for temperatures above the deconfinement temperature in SU(2) and SU(3) gauge theory. By analyzing its finite size behaviour, this is found to be exactly zero in the thermodynamical limit for any T > T_c whenever the magnetic charge of the operator is different from zero. These results show that magnetic charge is superselected in the hot phase of quenched QCD.Comment: 4 pages, 6 figures, revtex

Analyticity in theta on the lattice and the large volume limit of the topological susceptibility

Non-analyticity of QCD with a \theta term at \theta=0 may signal a spontaneous breaking of both parity and time reversal invariance. We address this issue by investigating the large volume limit of the topological susceptibility $\chi$ in pure SU(3) gauge theory. We obtain an upper bound for the symmetry breaking order parameter and, as a byproduct, the value \chi=(173.4(+/- 0.5)(+/- 1.2)(+1.1 / -0.2) MeV)^4 at \beta=6 (a approx= 0.1 fermi). The errors are the statistical error from our data, the one derived from the value used for \Lambda_L and an estimate of the systematic error respectively.Comment: 15 pages, corrected typos, added 1 reference, minor changes in tex