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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 236783, 15 pages
http://dx.doi.org/10.5402/2012/236783
Research Article

Evolving Center-Vortex Loops

Institut für Theoretische Physik, Universität Karlsruhe (TH), Kaiserstraße 12, 76131 Karlsruhe, Germany

Received 7 December 2011; Accepted 29 March 2012

Academic Editors: J. Bičák and M. Ehrnström

Copyright © 2012 Julian Moosmann and Ralf Hofmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider coarse-graining applied to nonselfintersecting planar centervortex loops as they emerge in the confining phase of an SU(2) Yang-Mills theory. Well-established properties of planar curve-shrinking predict that a suitably defined, geometric effective action exhibits (mean-field) critical behavior when the conformal limit of circular points is reached. This suggests the existence of an asymptotic mass gap. We demonstrate that the initially sharp mean center-of-mass position in a given ensemble of curves develops a variance under the flow as is the case for a position eigenstate in free-particle quantum mechanics under unitary time evolution. A possible application of these concepts is an approach to high- 𝑇 𝑐 superconductivity based (a) on the nonlocal nature of the electron (1 fold selfintersecting center-vortex loop) and (b) on planar curve-shrinking flow representing the decrease in thermal noise in a cooling cuprate.