Monopoles and Dyons in Non-Commutative Geometry

TL;DR

This paper explores magnetic monopoles and dyons in non-commutative geometry using brane constructions, revealing their supersymmetry properties, masses, and stability in relation to commutative theories.

Contribution

It demonstrates how non-commutative effects influence monopoles and dyons, including supersymmetry preservation and mass equivalence with commutative counterparts.

Findings

D-strings stretch at angles depending on background fields.

(p,q)-dyons and string junctions are stable but break all supersymmetry.

Masses of monopoles and dyons match their commutative equivalents.

Abstract

Taking advantage of the equivalence between supersymmetric Yang-Mills theory on non-commutative spaces and the field theory limit of D3-branes in the background of NSNS 2-form field, we investigate the static properties of magnetic monopoles and dyons using brane construction techniques. When parallel D3-branes are separated by turning on a Higgs vacuum expectation value, D-strings will stretch between them at an angle which depends on the value of the background 2-form potential. These states preserve half of the supersymmetries and have the same masses as their commutative counterparts in the field theory limit. We also find stable (p,q)-dyons and string junctions. We find that they do not preserve any supersymmetry but have the same masses as their commutative counterparts. In the field theory limit, the (p,q)-dyons and the string junctions restore 1/2 and 1/4 of the 16 supersymmetries, respectively.