Rare Decay Modes of Quarter BPS Dyons

TL;DR

This paper investigates the stability of quarter BPS dyons in N=4 string theories, showing that certain decay channels do not cause spectrum jumps in generic moduli space regions.

Contribution

It demonstrates that decay subspaces for quarter BPS dyons are of high codimension, ensuring the dyon spectrum remains continuous across the moduli space.

Findings

Decay subspaces are of codimension two or more.

No spectrum jumps occur for generic moduli space points.

Decay channels into quarter and half BPS dyons are suppressed.

Abstract

The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is known to jump across walls of marginal stability on which a quarter BPS dyon can decay into a pair of half BPS dyons. We show that as long as the electric and magnetic charges of the original dyon are primitive elements of the charge lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes marginally unstable against decay into a pair of quarter BPS dyons or a half BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any pair of generic points in the moduli space can be connected by a path avoiding these subspaces and there is no jump in the spectrum associated with these subspaces.