https://doi.org/10.1140/epjc/s10052-018-5663-x
Regular Article - Theoretical Physics
Effective theory of the D = 3 center vortex ensemble
1
Instituto de Física, Universidade Federal Fluminense, Campus da Praia Vermelha, Niterói, RJ, 24210-340, Brazil
2
Institut für Theoretische Physik, Auf der Morgenstelle 14, 72076, Tübingen, Germany
* e-mail: oxman@if.uff.br
Received:
17
January
2018
Accepted:
21
February
2018
Published online:
3
March
2018
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.
© The Author(s), 2018