Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method

TL;DR

This paper introduces an iterative method based on an extended Hopf fibration to generate singular solutions to the Seiberg-Witten and Freund equations on flat space, expanding the understanding of these solutions beyond known cases.

Contribution

It presents a novel iterative approach to construct singular solutions to the Seiberg-Witten and Freund equations on flat space using an extended Hopf fibration.

Findings

Generated explicit examples of singular solutions

Demonstrated the effectiveness of the iterative method

Extended the class of known solutions to these equations

Abstract

Although it is well known that the Seiberg-Witten equations do not admit nontrivial $L^2$ solutions in flat space, singular solutions to them have been previously exhibited -- either in $R^3$ or in the dimensionally reduced spaces $R^2$ and $R^1$ -- which have physical interest. In this work, we employ an extension of the Hopf fibration to obtain an iterative procedure to generate particular singular solutions to the Seiberg-Witten and Freund equations on flat space. Examples of solutions obtained by such method are presented and briefly discussed.