Non-abelian Dyons

TL;DR

This paper explores the quantum states of non-abelian monopoles called dyons in Yang-Mills-Higgs theory, revealing their electric-magnetic properties and how they relate to the underlying gauge symmetry and representation theory.

Contribution

It provides a detailed analysis of non-abelian dyons in SU(3) gauge theory, linking their properties to the representation theory of a semi-direct product group.

Findings

Dyons exhibit a complex interplay of magnetic and electric charges.

Representation theory captures the structure of dyonic states.

Implications for duality and fusion rules are discussed.

Abstract

The dyonic quantum states of magnetic monopoles in Yang-Mills-Higgs theory with a non-abelian unbroken gauge group display a subtle interplay between magnetic and electric properties. This is described in detail in the theory with the gauge group SU(3) broken to U(2), and shown to be captured by the representation theory of the semi-direct product of U(2) with R^4. The implications of this observation for the fusion rules and electric-magnetic duality properties of dyonic states are pointed out.