Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory

Abstract

We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects. We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non--perturbative contribution to the total energy.

arXiv comment26 pages, 20 eps-files combined to 8 figures, minor typos corrected. Version to be published in Nucl. Phys. B

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• Quantum stabilization of Z-strings, a status report on D=3+1 dimensions
• Gauge Invariance and Vacuum Energies of Non-Abelian String-Configurations
• Vacuum Energies of Non--Abelian String--Configurations in 3+1 Dimensions
• Quantum fluctuations around low-dimensional topological defects
• One-loop fluctuations of semi-local self-dual vortices
• Isospin Invariance and the Vacuum Polarization Energy of Cosmic Strings
• Quantum Stabilization of a Closed Nielsen-Olesen String
• Quantum Stabilization of Cosmic Strings
• Cosmic Strings Stabilized by Quantum Fluctuations