Spectral curves and the mass of hyperbolic monopoles

TL;DR

This paper explores how the mass parameter influences the spectral data of hyperbolic monopoles, providing explicit formulas for charge two and methods to compute masses for symmetric higher-charge cases, connecting to Euclidean monopoles.

Contribution

It offers an explicit description of mass dependence for hyperbolic monopoles and introduces techniques to compute masses for symmetric higher-charge spectral curves.

Findings

Explicit mass dependence for charge two hyperbolic monopoles.

Method to compute monopole mass for symmetric higher-charge spectral curves.

Euclidean monopoles obtained as a limit of hyperbolic monopoles with infinite mass.

Abstract

The moduli spaces of hyperbolic monopoles are naturally fibred by the monopole mass, and this leads to a nontrivial mass dependence of the holomorphic data (spectral curves, rational maps, holomorphic spheres) associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit description of this dependence for general hyperbolic monopoles of magnetic charge two. In addition, we show how to compute the monopole mass of higher charge spectral curves with tetrahedral and octahedral symmetries. Spectral curves of euclidean monopoles are recovered from our results via an infinite-mass limit.