The Construction of Monopoles

TL;DR

This paper presents a new algebraic method to construct Higgs and gauge fields for BPS monopoles directly from spectral curves, bypassing the need to solve gauge constraints, thus solving a long-standing problem.

Contribution

It introduces a novel approach to reconstruct monopole fields algebraically from spectral curves, eliminating the need for solving gauge constraints.

Findings

Constructed monopole fields directly from spectral curves.

Provided an algebraic reconstruction method analogous to instanton theory.

Solved a longstanding open problem in monopole theory.

Abstract

We show that the Higgs and gauge fields for a BPS monopole may be constructed directly from the spectral curve without having to solve the gauge constraint needed to obtain the Nahm data. The result is the analogue of the instanton result: given ADHM data one can reconstruct the gauge fields algebraically together with differentiation. Here, given the spectral curve, one can similarly reconstruct the Higgs and gauge fields. This answers a problem that has remained open since the discovery of monopoles.