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

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.

arXiv commentLatex file, 29 pages, 10 Tables, 10 Figures. Version to appear in Nuclear Physics B

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• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Quantum fluctuations around low-dimensional topological defects
• On the semiclassical mass of ${\mathbb{S}}^2$-kinks
• Higgs phase in a gauge $\mathbf{U}(1)$ non-linear ${\mathbf{CP}}^1$-model. Two species of BPS vortices and their zero modes
• One-loop fluctuations of semi-local self-dual vortices
• Kink mass quantum shifts from SUSY quantum mechanics
• Two species of semi-local cosmic strings in Abelian gauged ${\mathbb{CP}}^2$-sigma models coupled to gravity