Knotted instantons from annihilations of monopole-instanton complex

TL;DR

This paper explores the decay of monopole-anti-monopole sheets in 5+1 dimensions, revealing the formation of stable, knotted instanton strings as a novel topological soliton after annihilation.

Contribution

It introduces the concept of knotted instantons formed from monopole-instanton annihilation, a new topological soliton in higher-dimensional gauge theories.

Findings

Monopole-anti-monopole pairs decay into closed instanton strings.

A new topological soliton, a knotted instanton, remains after annihilation.

The knotted instanton has codimension five and topological stability.

Abstract

Monopoles and instantons are sheets (membranes) and strings in d=5+1, respectively, and instanton strings can terminate on monopole sheets. We consider a pair of monopole and anti-monopole sheets which is unstable to decay and results in a creation of closed instanton strings. We show that when an instanton string is stretched between the monopole sheets, there remains a new topological soliton of codimension five after the pair annihilation, i.e., a twisted closed instanton string or a knotted instanton.