Higgs potential and confinement in Yang-Mills theory on exotic R^4

Abstract: We show that pure SU(2) Yang-Mills theory formulated on certain exotic R^4 from the radial family shows confinement. The condensation of magnetic monopoles and the qualitative form of the Higgs potential are derived from the exotic R^4, e. A relation between the Higgs potential and inflation is discussed. Then we obtain a formula for the Higgs mass and discuss a particular smoothness structure so that the Higgs mass agrees with the experimental value. The singularity in the effective dual U(1) potential has its cause by the exotic 4-geometry and agrees with the singularity in the maximal abelian gauge scenario. We will describe the Yang-Mills theory on e in some limit as the abelian-projected effective gauge theory on the standard R^4. Similar results can be derived for SU(3) Yang-Mills theory on an exotic R^4 provided dual diagonal effective gauge bosons propagate in the exotic 4-geometry.