Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

TL;DR

This paper develops a modified heat kernel expansion to accurately compute quantum corrections to vortex masses and string tensions in the Abelian Higgs model, revealing weak repulsive forces due to vacuum fluctuations.

Contribution

It introduces a new regularization technique to handle zero mode divergences, enabling precise one-loop quantum correction calculations for vortices and flux tubes.

Findings

Quantum corrections induce weak repulsive forces between vortices.

Modified GdW expansion reduces infrared divergence issues.

One-loop string tension shifts are quantitatively determined.

Abstract

Spectral heat kernel/zeta function regularization procedures are employed in this paper to control the divergences arising from vacuum fluctuations of Bogomolnyi-Prasad-Sommerfield vortices in the Abelian Higgs model. Zero modes of vortex fluctuations are the source of difficulties appearing when the standard Gilkey-de Witt expansion is performed. A modified GdW expansion is developed to diminish the impact of the infrared divergences due to the vortex zero modes. With this new technique at our disposal we compute the one-loop vortex mass shift in the planar AHM and the quantum corrections to the string tension of the magnetic flux tubes living in three dimensions. In both cases it is observed that weak repulsive forces surge between these classically non interacting topological defects caused by vacuum quantum fluctuations.