A Necessary Condition for the Existence of SW-Monopoles
Mathematical Physics
2016-09-07 v1 Differential Geometry
math.MP
Abstract
Originally, the SW-equations discovered by Seiberg-Witten are 1st-order PDE, which solutions (A,\phi), with \phi\ne 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 spin^{c} class \alpha, the minimum is always attained by this sort of solution. In fact, there are only a finite number of \alpha such that the minimum is a SW-monopole. We show a necessary condition to be satisfied by the class \alpha in order to the minimum be a SW-monopole.
Cite
@article{arxiv.math-ph/0205008,
title = {A Necessary Condition for the Existence of SW-Monopoles},
author = {Celso M. Doria},
journal= {arXiv preprint arXiv:math-ph/0205008},
year = {2016}
}