Evolving center-vortex loops

TL;DR

This paper explores the geometric and critical behavior of center-vortex loops in SU(2) Yang-Mills theory, suggesting a link to mass gap emergence and potential applications in high-temperature superconductivity.

Contribution

It introduces a geometric coarse-graining method for vortex loops, revealing critical behavior and variance development akin to quantum mechanics, with implications for superconductivity.

Findings

Center-vortex loops exhibit critical behavior near conformal limits.

Variance in vortex loop position develops similarly to quantum eigenstates.

Potential application to high-$T_c$ superconductivity through vortex dynamics.

Abstract

We consider coarse-graining applied to nonselfintersecting planar center-vortex 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.