Dyon - Monopole Bound States, Self-Dual Harmonic Forms on the Multi-Monopole Moduli Space, and SL(2,Z) Invariance in String Theory

TL;DR

This paper demonstrates the existence of supersymmetric bound states of monopoles and dyons in string theory, linking SL(2,Z) duality to harmonic forms on monopole moduli spaces, with explicit construction for two monopoles.

Contribution

It provides an explicit construction of self-dual harmonic forms on the two-monopole moduli space, establishing the existence of bound states required by SL(2,Z) duality.

Findings

Explicit harmonic form constructed on two-monopole moduli space

Proof of bound states existence in two-monopole sector

Supports SL(2,Z) duality in string theory

Abstract

Existence of SL(2,Z) duality in toroidally compactified heterotic string theory (or in the N=4 supersymmetric gauge theories), that includes the strong weak coupling duality transformation, implies the existence of certain supersymmetric bound states of monopoles and dyons. We show that the existence of these bound states, in turn, requires the existence of certain normalizable, (anti-)self-dual, harmonic forms on the moduli space of BPS multi-monopole configurations, with specific symmetry properties. We give an explicit construction of this harmonic form on the two monopole moduli space, thereby proving the existence of all the required bound states in the two monopole sector.