Some aspects are discussed of the mechanism of color confinement in QCD by condensation of magnetic monopoles in the vacuum.
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.
The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, mus
t have a gauge-invariant status. It is proved, by use of non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and controllable way.
The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian
Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
A natural explanation of confinement can be given in terms of symmetry. Since color symmetry is exact, the candidate symmetry is dual and related to homotopy,i.e., in (3+1)d, to magnetic charge conservation. A set of r abelian tHooft-like tensors (r
= rank of the gauge group) can be defined and the dual charge is a violation of the corresponding Bianchi identities. It is shown that this is equivalently described by non-abelian Bianchi identities.
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 QCD with a generic compact gauge group. This issue is relevant to the understanding of color confinement in terms of dual symmetry.
We study monopoles and corresponding t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of color confinement.
