4d ensembles of percolating center vortices and monopole defects: the emergence of flux tubes with N-ality and gluon confinement

Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice ${\rm SU}(N)$ 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 center-element 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 ${\rm SU}(N) \to {\rm Z}(N)$ 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).