The Moduli Space of Many BPS Monopoles for Arbitrary Gauge Groups

TL;DR

This paper investigates the structure of the moduli space for multiple BPS monopoles in various gauge theories, deriving the asymptotic metric and providing evidence that it is exact for certain cases, extending known results.

Contribution

It generalizes the understanding of monopole moduli spaces to arbitrary gauge groups and multiple monopoles, proposing the asymptotic metric as the exact solution in these cases.

Findings

Asymptotic metric matches the exact metric for two monopoles.

The asymptotic form remains nonsingular for all monopole separations.

Conjecture that the asymptotic metric is exact for multiple monopoles in these theories.

Abstract

We study the moduli space for an arbitrary number of BPS monopoles in a gauge theory with an arbitrary gauge group that is maximally broken to $U(1)^k$. From the low energy dynamics of well-separated dyons we infer the asymptotic form of the metric for the moduli space. For a pair of distinct fundamental monopoles, the space thus obtained is $R^3 \times(R^1\times {\cal M}_0)/Z$ where ${\cal M}_0$ is the Euclidean Taub-NUT manifold. Following the methods of Atiyah and Hitchin, we demonstrate that this is actually the exact moduli space for this case. For any number of such objects, we show that the asymptotic form remains nonsingular for all values of the intermonopole distances and that it has the symmetries and other characteristics required of the exact metric. We therefore conjecture that the asymptotic form is exact for these cases also.