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Killing spinors are Killing vector fields in Riemannian Supergeometry

Alekseevsky, D. V., Cortes, V., Devchand, C., & Semmelmann, U. (1997). Killing spinors are Killing vector fields in Riemannian Supergeometry.

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killing spinors.pdf (Preprint), 178KB
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### Creators

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Creators:
Alekseevsky, D. V., Author
Cortes, V., Author
Devchand, C.1, Author
Semmelmann, U., Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Abstract: A supermanifold M is canonically associated to any pseudo Riemannian spin manifold (M_0,g_0). Extending the metric g_0 to a field g of bilinear forms g(p) on T_p M, p\in M_0, the pseudo Riemannian supergeometry of (M,g) is formulated as G-structure on M, where G is a supergroup with even part G_0\cong Spin(k,l); (k,l) the signature of (M_0,g_0). Killing vector fields on (M,g) are, by definition, infinitesimal automorphisms of this G-structure. For every spinor field s 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 if s is a twistor spinor. In particular, any Killing spinor s defines a Killing vector field X_s.

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Language(s): eng - English
Dates: 1997-04
Publication Status: Published in print
Pages: -
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Rev. Method: -
Identifiers: eDoc: 330151
Degree: -

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