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 that extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms that enter into this structure and we give a lot of examples.

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Cited by in corpus (14)

• Superconformal quantum field theory in curved spacetime
• Conformal symmetry superalgebras
• Supersymmetric Killing Structures
• Twistor spinors and extended conformal superalgebras
• Generalized symmetry superalgebras
• SUSY structures on deformed supermanifolds
• Killing Vector Fields and Superharmonic Field Theories
• Superizations of Cahen-Wallach symmetric spaces and spin representations of the Heisenberg algebra
• The Torsion of Spinor Connections and Related Structures
• A family of non-restricted $D=11$ geometric supersymmetries
• Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds
• Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields
• Connections on Cahen-Wallach spaces
• Rigidity of Killing-Yano and conformal Killing-Yano superalgebras