Supersymmetric Killing Structures
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 nonflat reduced space. We examine in detail the additional terms which enter into this structure and we give a lot of examples.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 April 2005
 DOI:
 10.1007/s0022000412772
 arXiv:
 arXiv:2001.03239
 Bibcode:
 2005CMaPh.255..419K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics
 EPrint:
 Comm. Math. Phys. 255 (2005) no. 2, 419467