One-loop corrections to the string tension of the vortex in the Abelian Higgs model

Abstract

We present an exact numerical computation of the one-loop correction of the string tension for the Nielsen-Olesen vortex in the Abelian Higgs model. The computations proceeds via the computation of the Euclidean Green's function for the gauge, Higgs and Faddeev-Popov fields using mode functions, and taking the appropriate trace. Renormalization is an essential part of this computation, it is done by removing leading order contributions from the numerical results so as to make these finite, and to add the divergent parts back, after suitable regularization and renormalization. We encounter and solve some problems which are specific to gauge theories and topological solutions. The corrections to the energy are found to be sizeable, but still smaller than the classical energy as long as g**2 is smaller than unity.

arXiv comment48 pages, 48 figures

Cited by in corpus (6)

• The semiclassical energy density of kinks and solitons
• Winding number dependence of quantum vortex energies at one-loop
• Quantum energies of BPS vortices in $D=2+1$ and $D=3+1$
• Vacuum polarization energy of a complex scalar field in a vortex background
• One-loop corrections to the Nielsen-Olesen vortex: collective oscillations
• One-loop corrections to the Nielsen-Olesen vortex: finite length