  We introduce a notion of twisted pure spinor in order to characterize, in a
unified way, all the special Riemannian holonomy groups just as a classical
pure spinor characterizes the special K\"ahler holonomy. Motivated by certain
curvature identities satisfied by manifolds admitting parallel twisted pure
spinors, we also introduce the Clifford monopole equations as a natural
geometric generalization of the Seiberg-Witten equations. We show that they
restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit
non-trivial solutions on manifolds with special Riemannian holonomy.

Differential Geometry