The Dirac Sea Contribution To The Energy Of An Electroweak String

TL;DR

This paper calculates how the Dirac sea affects the energy and stability of an electroweak string, showing that fermionic effects generally destabilize it unless positive energy states are populated to enhance stability.

Contribution

It provides a systematic calculation of the fermionic energy shift due to the Dirac sea in electroweak strings, highlighting the destabilizing effect and conditions for stabilization.

Findings

Dirac sea lowers the fermionic ground state energy of the string.

Populating positive energy states can offset destabilization.

Fermions can enhance string stability with sufficient bound state population.

Abstract

We present a systematic determination of the order hbar fermionic energy shift when an electroweak string is perturbed. We show that the combined effect of zero modes, bound states and continuum states is to lower the total fermionic ground state energy of the string when the Higgs instability of the string is excited. The effect of the Dirac sea is thus to destabilise the string. However, this effect can be offset by populating positive energy states. Fermions enhance the stability of an electroweak string with sufficiently populated fermionic bound states.