The number and the location of the monopoles observed on the lattice in QCD configurations happens to depend strongly on the choice of the gauge used to expose them, in contrast to the physical expectation that monopoles be gauge invariant objects. I
t is proved by use of the non abelian Bianchi identities (NABI) that monopoles are indeed gauge invariant, but the method used to detect them depends, in a controllable way, on the choice of the abelian projection. Numerical checks are presented.
Magnetic degrees of freedom are manifested through violations of the Bianchi identities and associated with singular fields. Moreover, these singularities should not induce color non-conservation. We argue that the resolution of the constraint is tha
t the singular fields, or defects are Abelian in nature. Recently proposed surface operators seem to represent a general solution to this constraint and can serve as a prototype of magnetic degrees of freedom. Some basic lattice observations, such as the Abelian dominance of the confining fields, are explained then as consequences of the original non-Abelian invariance.
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
We study monopoles and corresponding t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of color confinement.
We present a model for string breaking based on the existence of chromoelectric flux tubes. We predict the form of the long-range potential, and obtain an estimate of the string breaking length. A prediction is also obtained for the behaviour with te
mperature of the string breaking length near the deconfinement phase transition. We plan to use this model as a guide for a program of study of string breaking on the lattice.
