On non-$L^2$ solutions to the Seiberg-Witten equations
C. Adam, B. Muratori, C. Nash
TL;DR
This paper clarifies a sign error in Freund's previous solution to the Seiberg-Witten equations, discusses the non-$L^2$ properties of solutions, and constructs a new class of solutions to these equations.
Contribution
It corrects a sign error in prior work and introduces a new class of solutions to the Seiberg-Witten equations.
Findings
Freund's solution has a sign error and is not a true solution.
The paper clarifies the non-$L^2$ nature of certain solutions.
A new class of solutions to the Seiberg-Witten equations is constructed.
Abstract
We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non- nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.
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