Massless monopole clouds and electric–magnetic duality

Abstract

We discuss the Montonen-Olive electric-magnetic duality for the BPS massless monopole clouds in N = 4 supersymmetric Yang-Mills theory with non-Abelian unbroken gauge symmetries. We argue that these low energy non-Abelian clouds can be identified as the duals of the infrared bremsstrahlung radiation of the non-Abelian massless particles. After we break the N = 4 supersymmetry to N = 1 by adding a superpotential, or to N = 0 by further adding soft breaking terms, these non-Abelian clouds will generally condense and screen the non-Abelian charges of the massive monopole probes. The effective mass of these dual non-Abelian states is likely to persist as we lower the energy to the QCD scale, if all the non-Abelian Higgs particles are massive. This can be regarded as a manifestation of the non-Abelian dual Meissner effect above the QCD scale, and we expect it to continuously connect with the confinement as we lower the supersymmetry breaking scale to the QCD scale.