Abstract:
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.
Keywords:
twisted spinor, pure spinor, parallel spinor, special Riemannian holonomy, Clifford monopole.
The first author was partially supported by grants from CONACyT, LAISLA (CONACyT-CNRS), INFN-Italy and IMU Berlin Einstein Foundation, and the second author was partially supported by grants from CONACyT and LAISLA (CONACyT-CNRS).
Received:February 12, 2019; in final form September 7, 2019; Published online September 22, 2019
Citation:
Rafael Herrera, Noemi Santana, “Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles”, SIGMA, 15 (2019), 072, 48 pp.