Nonlinear electrodynamics is skilled with knots

TL;DR

This paper demonstrates that nonlinear electrodynamics can support universal knotted solutions in vacuum, explores their interaction with probe waves, and suggests optical experiments as a potential way to observe these knots.

Contribution

It shows that knotted solutions are supported in nonlinear electrodynamics regardless of the specific Lagrangian, and connects their behavior to Robinson congruences for potential experimental detection.

Findings

Knotted solutions exist in nonlinear electrodynamics independent of the Lagrangian.

Interaction with probe waves can be described via Robinson congruences.

Optical setups with intense fields could enable experimental observation of knots.

Abstract

The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, we argue that optical arrangements endowed with intense background fields could be the natural place to look for the knots experimentally.