Monopoles and Dyons in Non-Commutative Geometry

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.