Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space

Abstract

The flow of shape eigenmodes of the small fluctuation operator around BPS 2-vortex solutions is calculated, as a function of the intervortex separation $2d$. For the rotationally-invariant 2-vortex, with $d=0$, there are three discrete modes; the lowest is non-degenerate and the upper two are degenerate. As $d$ increases, the degeneracy splits, with one eigenvalue increasing and entering the continuous spectrum, and the other decreasing and asymptotically coalescing with the lowest eigenvalue, where they jointly become the eigenvalue of the 1-vortex radial shape mode. The behaviour of the eigenvalues near $d=0$ is clarified using a perturbative analysis, and also in light of the 2-vortex moduli space geometry.

12 pages, 8 figures

References in corpus (1)

• Collective coordinate model of kink-antikink collisions in ${\varphi }^4$ theory

Cited by in corpus (3)

• Collective Coordinate Models for 2-Vortex Shape Mode Dynamics
• Spectral wall in collisions of excited Abelian Higgs vortices
• Dissecting normal modes of vibration on vortices in Ginzburg-Landau superconductors