Hyperbolic vortices with large magnetic flux

TL;DR

This paper studies large magnetic flux abelian BPS vortices in hyperbolic space, providing explicit solutions and comparing them with magnetic bag approximations, revealing multi-layer vortex structures.

Contribution

It introduces exact multi-layer solutions for large flux BPS vortices in hyperbolic space, validating magnetic bag predictions with explicit formulas.

Findings

Exact vortex solutions analogous to magnetic bags are constructed.

Multi-layer vortex configurations are explicitly realized.

Comparison confirms the magnetic bag approximation's validity.

Abstract

There has been some recent interest in the study of non-abelian BPS monopoles in the limit of large magnetic charge. Most investigations have used a magnetic bag approximation, in which spherical symmetry is assumed within an abelian description. In particular, this approach has been used to suggest the existence of two types of magnetic bag, with differing distributions of the zeros of the Higgs field, together with multi-layer structures, containing several magnetic bags. This paper is concerned with the analogous situation of abelian BPS vortices in the hyperbolic plane, in the limit of large magnetic flux. This system has the advantage that explicit exact solutions can be obtained and compared with a magnetic bag approximation. Exact BPS vortex solutions are presented that are analogous to the two types of magnetic bags predicted for BPS monopoles and it is shown that these structures can be combined to produce exact multi-layer solutions.