Confinement and monopole condensation: some properties of the disorder parameter

We demonstrate that the disorder parameter $$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $\mu$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).Comment: Lattice2001(confinement) proceeding

Theory of color confinement: state of the art

The existing evidence for dual superconductivity as mechanism of color confinement is reviewed. We also discuss what is known on the dual excitations, which produce confinement by condensation, and what are the open problem

A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation

Let $X$ be a fuzzy set--valued random variable (\frv{}), and \huku{X} the family of all fuzzy sets $B$ for which the Hukuhara difference X\HukuDiff B exists $\mathbb{P}$--almost surely. In this paper, we prove that $X$ can be decomposed as X(\omega)=C\Mink Y(\omega) for $\mathbb{P}$--almost every $\omega\in\Omega$, $C$ is the unique deterministic fuzzy set that minimizes $\mathbb{E}[d_2(X,B)^2]$ as $B$ is varying in \huku{X}, and $Y$ is a centered \frv{} (i.e. its generalized Steiner point is the origin). This decomposition allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink \indicator{\xi(\omega)} for some deterministic fuzzy convex set $M$ and some random element in \Banach). In particular, $X$ is an \frv{} translation if and only if the Aumann expectation $\mathbb{E}X$ is equal to $C$ up to a translation. Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision; references, affiliation and acknowledgments added. Submitted versio

Condensation of vortices and disorder parameter in 3d Heisenberg model

The 3d Heisenberg model is studied from a dual point of view. It is shown that the disordered phase corresponds to condensation of vortices in the vacuum, and the critical indices are computed from the corresponding disorder parameter.Comment: LATTICE98(spin

A dual view of the 3d Heisenberg model and the abelian projection

The Heisenberg model in 3d is studied from a dual point of view. It is shown that it can have vortex configurations, carrying a conserved charge(U(1) symmetry). Vortices condens in the disordered phase. A disorder parameter \leftangle\mu\rightangle is defined dual to the magnetization \leftangle\vec n\rightangle, which signals condensation of vortices, i.e. spontaneous breaking of the dual U(1) symmetry. This study sheds light on the procedure known as abelian projection in non abelian gauge theories.Comment: LateX, 15 pages, 3 figure

The abelian projection revisited

Abelian projection is reanalysed in the frame of the SU(N) Higgs model. The extension to QCD is discussed. It is shown that dual superconductivity of the vacuum is an intrinsic property independent of the choice of the abelian projection.Comment: 3 pages, 1 figure, Lattice2003(topology

Chiral transition and deconfinement in N_f = 2 QCD

The transition is studied by means of a disorder parameter detecting condensation of magnetic monopoles in the vacuum. The deconfining transition is found to coincide with the chiral transition and the susceptibility \rho, related to the disorder parameter, is consistent with a first order phase transition.Comment: 3 pages, 2 figures. Poster presented at Lattice2004(topology), Fermilab, June 21-26, 200