The Sen conjecture for fundamental monopoles of distinct type

TL;DR

This paper constructs a specific harmonic form on the moduli space of distinct fundamental BPS monopoles, supporting Sen's S-duality conjecture, and analyzes the geodesic structure of the space.

Contribution

It provides the first explicit harmonic form on the moduli space of fundamental monopoles for any Lie group, confirming aspects of Sen's conjecture.

Findings

Existence of a middle-dimensional harmonic form on the moduli space.

Confirmation of no closed or bound geodesics in the moduli space.

Support for Sen's S-duality conjecture.

Abstract

I exhibit a middle-dimensional square integrable harmonic form on the moduli space of distinct fundamental BPS monopoles of an arbitrary Lie group. This is in accord with Sen's S-duality conjecture. I also show that the moduli space has no closed or bound geodesics.