Vortices as degenerate metrics
High Energy Physics - Theory
2021-06-30 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L^2-metric on the moduli space upon restriction to a class of submanifolds.
Cite
@article{arxiv.1212.3561,
title = {Vortices as degenerate metrics},
author = {J. M. Baptista},
journal= {arXiv preprint arXiv:1212.3561},
year = {2021}
}
Comments
15 pages; v2: expanded introduction and additional observations in the last section