Moduli of Monopole Walls and Amoebas

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.