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

Rafael Herrera ; Noemi Santana

Symmetry, integrability and geometry: methods and applications, Tome 15 (2019)

Résumé

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 Kähler 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.

Détail

Keywords: twisted spinor, pure spinor, parallel spinor, special Riemannian holonomy, Clifford monopole.

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