Center vortices as rigid strings

TL;DR

This paper demonstrates that the effective action of center vortices in SU(2) lattice gauge theory resembles that of rigid strings, with curvature correlations persisting in the continuum limit, suggesting a possible role for localized fields like monopoles.

Contribution

It establishes a strong correlation between vortex action and curvature, proposing rigid string models as effective descriptions and exploring monopoles as potential localized fields.

Findings

Vortex action correlates with extrinsic and internal curvature.

Rigid string action reproduces geometric vortex properties.

Monopoles may serve as localized fields inducing rigidity.

Abstract

It is shown that the action associated with center vortices in SU(2) lattice gauge theory is strongly correlated with extrinsic and internal curvatures of the vortex surface and that this correlation persists in the continuum limit. Thus a good approximation for the effective vortex action is the action of rigid strings, which can reproduce some of the observed geometric properties of center vortices. It is conjectured that rigidity may be induced by some fields localized on vortices, and a model-independent test of localization is performed. Monopoles detected in the Abelian projection are discussed as natural candidates for such two-dimensional fields.