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ID: 330151.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Killing spinors are Killing vector fields in Riemannian Supergeometry
Authors:Alekseevsky, D. V.; Cortes, V.; Devchand, C.; Semmelmann, U.
Language:English
Date of Publication (YYYY-MM-DD):1997-04
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:submitted
Document Type:Other
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
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