Some aspects of topological solitons in supersymmetric gauge theories

Abstract

Classical and quantum physics of some topological solitons in supersymmetric gauge theories are investigated. When the supersymmetry algebra is centrally extended, there exists a lower bound (BPS bound) in the mass spectrum given by the central charge. BPS solitons saturate this bound. Dyonic instanton is a BPS soliton in 5-dimensional supersymmetric Yang-Mills theories. We study Higgs field configurations of dyonic instantons in spontaneously broken 5-dimensional $SU(2)$ Yang-Mills theory, and find the D-brane interpretation of such configurations as supretubes stretching between two parallel D4-branes. Then, we turn our eyes to BPS vortices in 3-dimensional $\N=2$ supersymmetric (abelian) Chern-Simons-Higgs theory, to study the quantum status of the BPS bound. It is shown explicitly that the saturation of the BPS bound remains to hold at the one-loop level.