Stability longevity and all that : false vacua and topological defects

TL;DR

This paper explores how solitons influence stability in theories with spontaneous symmetry breaking, demonstrating quantum stabilization of unstable solutions and cosmic strings catalyzing vacuum decay.

Contribution

It presents novel examples of quantum stabilization of unstable solitons and cosmic strings triggering vacuum decay, expanding understanding of topological defects in field theories.

Findings

Unstable topological solutions can be stabilized by fractional fermion numbers.

Cosmic strings can induce decay of metastable vacua by acting as nucleation sites.

Numerical calculations confirm the existence of instantons mediating vacuum transitions.

Abstract

I present two interesting studies related to the role of solitons in theories with spontaneous symmetry breaking. Quantised fermions coupled to solitons are known to induce fractional fermion number. I present an example where an unstable topological solution binding a zero mode of a majorana fermion gets stabilised due to the induced fractional number. Thus neither is the cosmic string stable nor is the fermion number conserved, yet the bound state then becomes stable due to Quantum Mechanics. The other phenomenon concerns a metastable vacuum getting destabilised due to the presence of a cosmic string. This happens because the scalar field signalling spontaneous symmetry breaking acquires a vacuum expectation value approaching its true vacuum value in the core of the string. Thus the string acts like a seed nucleating the true vacuum. The instanton mediating between the false vacuum and the exit point into the true vacuum is shown to exist and graphically displayed through a numeric calculation. T. Padmanabhan has been a long time friend and was collaborator for early investigations in this direction. I review these works done subsequently with other collaborators as a felicitation to him on his sixtieth birthday.