G. Paffuti

Color confinement and dual superconductivity of the vacuum. IV

SUMMARY A scaling analysis is made of the order parameter describing monopole condensation at the deconfining transition of N_f=2 QCD around the chiral point. In accordance with scaling properties of the specific heat, studied in a previous paper, scaling is consistent with a first order transition. The status of dual superconductivity of the vacuum as a mechanism of color confinement is reviewed.

Detecting dual superconductivity in the ground state of gauge theory

Abstract We explicitly construct a monopole creation operator: its vacuum expectation value is a disorder parameter for dual superconductivity, in that 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.

Colour confinement as dual Meissner effect:

Abstract We demonstrate that confinement in SU (2) gauge theory is produced by dual superconductivity of the vacuum. We show that for T T c (temperature of the deconfining phase transition) the U (1) symmetry related to monopole charge conservation is spontaneously broken; for T > T c the symmetry is restored.

SU(2)

Abstract Dual superconductivity in the confining phase of gauge theories is discussed in terms of a disorder parameter which vanishes in normal phase and is different from zero in the superconducting phase.

gauge theory

Abstract New accurate Monte Carlo data are used to determine the gluon condensation parameter 〈( α π ) Σ a,μν G μν a G μν a 〉 for SU(2) gauge theory. The procedure used proves to be correct, and the result confirms previous determinations.

A disorder parameter for dual superconductivity in gauge theories

Abstract A disorder parameter is constructed which signals the condensation of vortices. The construction is tested by numerical simulations.

Precise determination of 〈(απ)Σα,μνGμνaGμνa〉 from lattice gauge theories

Abstract 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.

Condensation of vortices in the XY model in 3D: A disorder parameter☆

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 condense in the disordered (demagnetized) phase. A disorder parameter

The abelian projection revisited

〈\ensuremath{\mu}〉

Dual view of the 3D Heisenberg model and the Abelian projection

is defined, dual to the magnetization