$S^1 \times S^2$ wormholes and topological charge

TL;DR

This paper explores Euclidean solutions with $S^1 imes S^2$ topology in Einstein-matter theories, revealing how they carry topological charges and influence cosmic string loop decay.

Contribution

It introduces new Euclidean solutions with topological charges in Einstein-matter theories and extends them to models with superconducting cosmic strings.

Findings

Solutions carry winding number and magnetic flux.

They violate a quasi-topological conservation law.

Contribute to decay of superconducting cosmic string loops.

Abstract

I investigate solutions to the Euclidean Einstein-matter field equations with topology $S^1 \times S^2 \times R$ in a theory with a massless periodic scalar field and electromagnetism. These solutions carry winding number of the periodic scalar as well as magnetic flux. They induce violations of a quasi-topological conservation law which conserves the product of magnetic flux and winding number on the background spacetime. I extend these solutions to a model with stable loops of superconducting cosmic string, and interpret them as contributing to the decay of such loops.