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We introduce a notion of twisted pure spinor in order to characterize, in aunified way, all the special Riemannian holonomy groups just as a classicalpure spinor characterizes the special K\"ahler holonomy. Motivated by certaincurvature identities satisfied by manifolds admitting parallel twisted purespinors, we also introduce the Clifford monopole equations as a naturalgeometric generalization of the Seiberg-Witten equations. We show that theyrestrict to the Seiberg-Witten equations in 4 dimensions, and that they admitnon-trivial solutions on manifolds with special Riemannian holonomy.

Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles