Zero helicity of Seifert framed defects

Abstract

Line defects are one-dimensional phase singularities (forming knots and links) that arise in a variety of physical systems. In these systems, isophase surfaces (Seifert surfaces) have the phase defects as boundary, and these Seifert surfaces define a framing of the normal bundle of each link component. We define the individual helicity for each component of a link singularity, and prove that each individual helicity is zero if and only if there exists a Seifert framing for the link. We extend these results to multi-armed defects. We prove that under anti-parallel reconnection of defect strands total twist is conserved.