Asymptotic Dynamics of Monopole Walls

TL;DR

This paper analyzes the long-distance behavior of U(N) monopole walls in Yang-Mills-Higgs theory, revealing how they split into subwalls and deriving an asymptotic metric for their moduli space.

Contribution

It introduces a novel geometric approach using Newton polytope and amoeba to study monopole wall dynamics and provides an explicit asymptotic metric for their moduli space.

Findings

Monopole walls split into subwalls at large moduli.

Long-distance interactions are abelian.

Derived an asymptotic metric for the moduli space.

Abstract

We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.