International Scholarly Research Network ISRN Mathematical Physics Volume 2012, Article ID 236783, 15 pages doi:10.5402/2012/236783 Research Article Evolving Center-Vortex Loops Julian Moosmann and Ralf Hofmann Institut f ¨ ur Theoretische Physik, Universit¨ at Karlsruhe (TH), Kaiserstraße 12, 76131 Karlsruhe, Germany Correspondence should be addressed to Ralf Hofmann, r.hofmann@thphys.uni-heidelberg.de Received 7 December 2011; Accepted 29 March 2012 Academic Editors: J. Biˇ c´ ak and M. Ehrnstr ¨ om Copyright q 2012 J. Moosmann and R. 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. We consider coarse-graining applied to nonselfintersecting planar centervortex loops as they emerge in the confining phase of an SU2 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. 1. Introduction The problem of how a confining ground state emerges in 4D nonabelian Yang-Mills theory was addressed by ’t Hooft in terms of the definition of an order parameter that is dual to the Wilson loop 1. The lattice-gauge-theory measurement as well as analytical model approaches to the ’t Hooft loop expectation was performed by several authors starting shortly thereafter 2–7. The according confinement scenario is a condensation of magnetic center vortices which induces narrow electric flux lines in between color-electric sources granting a potential which rises sufficiently rapid with an increasing distance of separation. Due to the absence of magnetic center monopoles the associated center vortices form closed flux loops. Four-dimensional SU2 Yang-Mills theory occurs in three phases: a deconfining, a preconfining, and a confining one. While the former two phases possess propagating gauge fields, a complete decoupling thereof takes place at a Hagedorn transition towards the confining phase 8–12. Namely, by the decay of a preconfining ground state, consisting of