An abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple-spinors

Abstract

We consider a variant of the Seiberg-Witten equations for multiple-spinors. The moduli space of solutions to our generalized Seiberg-Witten equations in the setting of Kähler surfaces has a direct relation with ASD connections of holomorphic vector bundle. Also in Kähler setting, we construct a numerical invariant from the equations that detects a notion of $\varphi -$stability of $SU(n)-$holomorphic vector bundles where $\varphi$ is some prescribed non-trivial holomorphic section.

An important technical mistake in the set-up of this variant of generalization to Seiberg-Witten equations was pointed out to the author. In particular, the equations are not elliptic as claimed. As a result, any statement about (or uses) regularity and transversality of the moduli space has to be disregarded. However, the moduli space is still compact