Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 072, 48 pages      arXiv:1506.07681

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

Rafael Herrera a and Noemi Santana b
a) Centro de Investigación en Matemáticas, A.P. 402, Guanajuato, Gto., C.P. 36000, México
b) Universidad Marista Valladolid, José Juan Tablada 1111, Santa Maria de Guido, 58090 Morelia, Mich., México

Received February 12, 2019, in final form September 07, 2019; Published online September 22, 2019

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.

Key words: twisted spinor; pure spinor; parallel spinor; special Riemannian holonomy; Clifford monopole.

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