Killing spinors are killing vector fields in Riemannian supergeometry
✍ Scribed by D.V. Alekseevsky; V. Cortés; C. Devchand; U. Semmelmann
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 880 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0393-0440
No coin nor oath required. For personal study only.
✦ Synopsis
A supermanifold M is canonically associated to any pseudo-Riemannian spin manifold (Ma, go). Extending the metric go to a field g of bilinear forms g(p) on TpM, p E MO, the pseudo-Riemannian supergeometry of (M, g) is formulated as G-structure on M, where G is a supergroup with even part Go 2 Spin(k, 1); (k, I) the signature of (Mu, go). Killing vector fields on (M, g) are, by definition, infinitesimal automorphisms of this G-structure. For every spinor fields there exists a corresponding odd vector field X,s on M. Our main result is that X,s is a Killing vector field on (M, g) if and only ifs is a twistor spinor. In particular, any Killing spinor s defines a Killing vector field X,.