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

Abstract

Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice SUðNÞ pure Yang-Mills theory. They successfully explain many properties of confinement and are strongly believed to capture the (infrared) path-integral measure. In this work, we initially motivate the presence of magnetic non-Abelian degrees of freedom in these ensembles. Next, we consider a simple Gaussian model to account for fluctuations. In this case, both center vortices and monopoles become relevant degrees in Wilson loop averages. These physical inputs are then implemented in an ensemble of percolating center vortices in four dimensions by proposing a measure to compute centerelement averages. The introduction of phenomenological information such as monopole tension, stiffness, and fusion leads to an effective YMH model with adjoint Higgs fields. If monopoles also condense, then the gauge group undergoes SUðNÞ → ZðNÞ SSB. This pattern has been proposed as a strong candidate to describe confinement. In the presence of external quarks, these models are known to be dominated by classical solutions, formed by flux tubes with N-ality as well as by confined dual monopoles (gluons).

Renormalizability of the center-vortex free sector of Yang-Mills theory

“…Recently, in Ref. [26], a phenomenological ensemble of percolating center-vortex worldsurfaces was generated by emergent gauge fields, which are the Goldstone modes in a condensate of center-vortex loops. The inclusion of monopoles with non-Abelian d.o.f.…”

“…Accordingly, S½A and the associated choice of S 0 is characterized by a distribution of center vortices and correlated monopoles with non-Abelian degrees of freedom (d.o.f.) [26]. Then, from this perspective, the Singer no-go theorem appears as the foundational basis for the YM theory to give place to a YM ensemble.…”

“…In the lattice, at asymptotic distances, they account for a Wilson loop area law with N-ality [30][31][32][33][34][35][36][37][38][39][40]. More recently, phenomenological ensembles containing the possible defects that characterize S 0 led to effective models that can accommodate the properties of the confining flux tube [26]. The aim of this work is to advance towards the establishment of a Yang-Mills ensemble from first principles.…”

BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric Yang-Mills-Higgs models

“…In Ref. [11] (see also [12]), the pure Yang-Mills sector of these models was associated with the continuum limit of an effective Wilson action with frustration. The latter generates an average of center elements which depends on the linking number between the external quark worldline C and plaquette configurations distributed on closed surfaces.…”

“…In Ref. [11], this type of nonoriented object was introduced by means of an ensemble of adjoint dual Wilson loops. Moreover, in the continuum, this sector induces a set of effective adjoint Higgs fields, while possible correlations between adjoint dual Wilson lines were related to effective Higgs interactions.…”