A raise of the Seiberg-Witten equations to Kaluza-Klein 5-manifolds
Authors: M. J. D. Hamilton
Summary: We think about Riemannian 4-manifolds (X,gX) with a Spin^c-structure and an appropriate circle bundle Y over X such that the Spin^c-structure on X lifts to a spin construction on Y. With respect to those constructions a spinor φ on X lifts to an untwisted spinor ψ on Y and a U(1)-gauge discipline A for the Spin^c-structure may be absorbed right into a Kaluza-Klein metric gAY on Y. We present that irreducible options (A,φ) to the Seiberg-Witten equations on (X,gX) for the given Spin^c-structure are equal to irreducible options ψ of a Dirac equation with cubic non-linearity on the Kaluza-Klein circle bundle (Y,gAY). As an software we think about options to the equations within the case of Sasaki 5-manifolds that are circle bundles over Kaehler-Einstein surfaces
