Evolving Center-Vortex Loops

Abstract EN

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-Tc 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.