# 4D ensembles of percolating center vortices and chains

## TL;DR

This paper reviews a measure for computing averages in a mixed ensemble of center vortices, chains, and monopoles, linking percolation and condensation phenomena to confinement features in a gauge theory.

## Contribution

It introduces a novel measure for center-element averages in a complex ensemble involving vortices, chains, and monopoles, connecting these to confinement mechanisms.

## Key findings

- Percolation of vortices and monopole condensation are described by a saddle point in a YMH model.
- The approach accounts for the Lüscher term and N-ality dependence of flux tubes.
- Confined gluons are incorporated within the ensemble framework.

## Abstract

In this work, we review a recently proposed measure to compute center-element averages in a mixed ensemble of center vortices and chains with non-Abelian d.o.f. and monopole fusion. When center vortices percolate and monopoles condense, the average is captured by a saddle point and collective modes in a YMH model. In this manner, the L\"uscher term, confining flux tubes with N-ality and confined gluons were accommodated in an ensemble picture.