Moduli of Monopole Walls and Amoebas

TL;DR

This paper investigates doubly-periodic monopoles, known as monopole walls, by analyzing their spectral data, moduli spaces, and symmetries, including an SL(2,Z) action related to the Nahm transform.

Contribution

It provides a detailed characterization of monopole wall moduli spaces and reveals an SL(2,Z) symmetry, connecting spectral data with the Nahm transform.

Findings

Determined spectral data for monopole walls

Computed dimensions of their moduli spaces

Identified an SL(2,Z) symmetry acting on monopole walls

Abstract

We study doubly-periodic monopoles, also called monopole walls, determining their spectral data and computing the dimensions of their moduli spaces. Using spectral data we identify the moduli, and compare our results with a perturbative analysis. We also identify an SL(2,Z) action on monopole walls, in which the S transformation corresponds to the Nahm transform.