Some properties of renormalons in gauge theories

We find the explicit operatorial form of renormalon-type singularities in abelian gauge theory. Local operators of dimension six take care of the first U.V. renormalon, non local operators are needed for I.R. singularities. In the effective lagrangian constructed with these operators non local imaginary parts appearing in the usual perturbative expansion at large orders are cancelled.Comment: 17 pages + uuencoded file with 7 figures, REVTeX, IFUP-TH-31-9

Magnetic monopoles in U(1)_4 Lattice Gauge Theory with Wilson action

We construct the Euclidean Green functions for the soliton (magnetic monopole) field in the U(1)_4 Lattice Gauge Theory with Wilson action. We show that in the strong coupling regime there is monopole condensation while in the QED phase the physical Hilbert space splits into orthogonal soliton sectors labelled by integer magnetic charge.Comment: 13 pages, LaTeX 2.09 (revtex), submitted to Communications in Mathematical Physic

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

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

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

Detecting Dual Superconductivity in the Ground State of Gauge Theory

We explicitly construct a monopole creation operator: its vacuum expectation value is an order parameter for dual superconductivity, in that, if different from zero, it signals a spontaneous breaking of the $U(1)$ symmetry corresponding to monopole charge conservation. This operator is tested by numerical simulations in compact $U(1)$ gauge theory. Our construction provides a general recipe for detection of the condensation of any topological soliton. In particular our operator can be used to detect dual superconductivity of the QCD vacuum.Comment: 10 pages, 3 figures avalaible on request. REVTE

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.

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

Condensation of vortices in the X-Y model in 3d: a disorder parameter

A disorder parameter is constructed which signals the condensation of vortices. The construction is tested by numerical simulations.Comment: 9 pages, 5 postscript figures, typset using REVTE