Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory

Abstract

We argue that in the infrared regime of continuum Yang-Mills theory, the possibility of a mass gap in the charged sector is closely associated with the center vortex sector. The analysis of the possible consequences of the ensembles of defects is done by showing that the description of center vortices and monopoles is naturally unified by means of a careful treatment of Cho decomposition. If on the one hand confinement is usually associated with monopole condensation in a compact abelian model, in this scenario, the previous decoupling of the offdiagonal degrees of freedom, for the abelian model dominate at large distances, can be understood as induced by a phase where center vortices become thick objects. Other important scenarios for correlated monopoles and center vortices, observed in lattice simulations, are also accomodated in our general formulation.

4D ensembles of percolating center vortices and monopole defects: The emergence of flux tubes withN-ality and gluon confinement

“…The simplest case corresponds to the fundamental representation ⃗w ¼ ⃗w i , i ¼ 1; …; N [44], which will be considered from now on. In chains, pairs of center vortex branches are matched by monopoles [16,52,57]. In this case, we can writeS…”

“…Chains were visualized as magnetic defects of a local color frame in Ref. [57]. Their relation to the observability of surfaces attached to the quark loop was discussed in Ref.…”

Coloured loops in 4D and their effective field representation

“…Some theoretical steps have already been taken in this direction. Monopoles, center vortices, as well as chains formed by them, can be accommodated as topological defects of different local bases in colour space [46]- [48]. Recently, we showed that ensembles of chains in 3D generate the effective model,…”

SU(N) → Z(N) dual superconductor models: the magnetic loop ensemble point of view

“…In ref. [22], motivated by previous work on the description of chains in the continuum, using defects of a local Lie basis [39], an analysis of center strings interpolated by monopoles was presented, pointing to some physical consequences. In this regard, lattice calculations predict a rich spectrum of exotic mesons.…”