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Supersymmetric Killing Structures

Authors
  • Klinker, Frank1
  • 1 University of Dortmund, Department of Mathematics, Dortmund, 44221, Germany , Dortmund
Type
Published Article
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Publication Date
Feb 04, 2005
Volume
255
Issue
2
Pages
419–467
Identifiers
DOI: 10.1007/s00220-004-1277-2
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our definition of supersymmetric Killing structures. The latter combines subspaces of vector fields and spinor fields, provided they fulfill certain field equations. This naturally leads to a superalgebra which extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms which enter into this structure and we give a lot of examples.

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