Spin and Dualization of SU(5) Dyons

TL;DR

This paper investigates the spectrum of stable SU(5) dyons that can be transformed into purely electric states, revealing new dualizable states with implications for the standard model fermions and predicting associated partner states.

Contribution

It provides solutions to the equations governing dualizable SU(5) dyons, linking them to standard model fermions and predicting new partner states and internal structures.

Findings

Existence of dualizable, half-integer spin SU(5) dyons matching standard model families

Prediction of dualizable, integer-spin partner states for each half-integer dyon

Electron-like dyons must have non-trivial color internal structure

Abstract

Motivated by the dual standard model, we study the angular momentum spectrum of stable SU(5) dyons that can be transformed into purely electric states by a suitable duality rotation i.e. are dualizable. The problem reduces to solving a Diophantine equation for the holomorphic charges in each topological sector, but the solutions also have to satisfy certain constraints. We show that these equations can be solved and sets of dualizable, half-integer spin SU(5) dyons can be found, each of which corresponds to a single family of the standard model fermions. We then find two predictions of the dual standard model. First, the family of half-integer spin, dualizable dyons is accompanied by a set of dualizable, integer-spin partner states. Secondly, the dyon corresponding to the electron must necessarily contain non-trivial color internal structure. In addition, we provide other general results regarding the spectrum of dualizable dyons and their novel properties, and extend the stability analysis of SU(5) monopoles used in the dual standard model so far to discuss the stability of the half-integer spin dyons.