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.
Highlights
Magnetic monopoles are attached to center vortices [23] and change the direction of the flux of center vortices [24].1 condensation of center vortices in the confined phase implies the condensation of magnetic monopoles and the dual Meissner effect
The ensemble of oriented center vortices is mapped onto an effective theory of a complex scalar field with a U(1) symmetry
In this paper we study the ensemble of closed center vortices in D = 3 exploiting the fact that the partition function of a gas of one dimensional objects can be represented by a complex scalar quantum field theory [37,38,39]
Summary
Magnetic monopoles are attached to center vortices [23] and change the direction of the flux of center vortices [24].1 condensation of center vortices in the confined phase implies the condensation of magnetic monopoles and the dual Meissner effect. The gross features of center projected Yang–Mills theory, like the emergence of the string tension or the deconfinement phase transition, can be reproduced in a center vortex model with an action given by the vortex area plus a penalty for the curvature of the vortices [33,34,35]. The latter accounts for the stiffness of the vortices.
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