4D ensembles of percolating center vortices and chains

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.Comment: 9 pages, 6 figures. Talk presented at the "XIII Quark Confinement and the Hadron Spectrum" conference (Confinement 2018), 31 July - 6 August 2018, Maynooth University, Irelan

Effective theory of the D = 3 center vortex ensemble

By means of lattice calculations, center vortices have been established as the infrared dominant gauge field configurations of Yang-Mills theory. In this work, we investigate an ensemble of center vortices in D = 3 Euclidean space-time dimension where they form closed flux loops. To account for the properties of center vortices detected on the lattice, they are equipped with tension, stiffness and a repulsive contact interaction. The ensemble of oriented center vortices is then mapped onto an effective theory of a complex scalar field with a U(1) symmetry. For a positive tension, small vortex loops are favoured and the Wilson loop displays a perimeter law while for a negative tension, large loops dominate the ensemble. In this case the U(1) symmetry of the effective scalar field theory is spontaneously broken and the Wilson loop shows an area law. To account for the large quantum fluctuations of the corresponding Goldstone modes, we use a lattice representation, which results in an XY model with frustration, for which we also study the Villain approximation.Comment: 23 page