Effective theory of the D = 3 center vortex ensemble

Abstract

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.

23 pages

References in corpus (5)

• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Dielectric function of the QCD vacuum
• Closed k-strings in SU(N) gauge theories : 2+1 dimensions
• A model of random center vortex lines in continuous 2+1-dimensional space-time
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Cited by in corpus (6)

• Branching of Center Vortices in SU(3) Lattice Gauge Theory
• 4d ensembles of percolating center vortices and monopole defects: the emergence of flux tubes with N-ality and gluon confinement
• 3D Yang-Mills confining properties from a non-Abelian ensemble perspective
• From center-vortex ensembles to the confining flux tube
• The infrared Yang-Mills wave functional due to percolating center vortices
• Study of Gribov Copies in the Yang-Mills ensemble