A Necessary Condition for the Existence of SW-Monopoles
Abstract
Originally, the SW-equations discovered by Seiberg-Witten are 1st-order PDE, which solutions (A,φ), with φ 0, are known as SW-monopoles. It is known that the solutions of these 1st-order eq correspond to the minimum of SW-functional. However, it is not true, that for all spinc class α, the minimum is always attained by this sort of solution. In fact, there are only a finite number of α such that the minimum is a SW-monopole. We show a necessary condition to be satisfied by the class α in order to the minimum be a SW-monopole.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.