Structure of Multi-Meron Knot Action

TL;DR

This paper investigates the structure of multi-meron knot actions in Yang-Mills and CP^1 Ginzburg-Landau models, deriving self-dual equations and analyzing energy bounds related to topological parameters like the Hopf invariant.

Contribution

It introduces a novel analysis of multi-meron knot structures, deriving self-dual equations without orientation constraints and linking knot size to topological invariants.

Findings

Self-dual equations derived without orientation assumptions

Energy bounds depend on topological parameters

Knot size in Faddeev-Niemi model linked to Hopf invariant

Abstract

We consider the structure of multi-meron knot action in the Yang-Mills theory and in the CP^1 Ginzburg-Landau model. Self-dual equations have been obtained without identifying orientations in the space-time and in the color space. The dependence of the energy bounds on topological parameters of coherent states in planar systems is also discussed. In particular, it is shown that a characteristic size of a knot in the Faddeev-Niemi model is determined by the Hopf invariant.