One loop corrections to the mass of self-dual semi-local planar topological solitons

TL;DR

This paper derives a formula for calculating one-loop quantum mass corrections to self-dual semi-local topological solitons in a generalized Abelian Higgs model, relevant to electroweak theory at a specific angle.

Contribution

It introduces a novel method combining canonical quantization and heat kernel/zeta function regularization for semi-classical mass shift calculations.

Findings

Derived a practical formula for one-loop mass shifts.

Applied the method to semi-local strings in a generalized Higgs model.

Connected the model to electroweak theory at a 90-degree mixing angle.

Abstract

A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU(2), and local (gauge), U(1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is of 90 degrees. The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.