One of C.Taubes' theorems says that for a symplectic 4-manifold with $b_2^+>1$, $\mathrm{Gr}(e)=0$ if $C_1(K).e-e.e\neq0$. This theorem is proved using Seiberg-Witten theory.
And my question is: can one prove this gauge-theory-freely?