# Supersymmetric Killing Structures

@article{Klinker2005SupersymmetricKS, title={Supersymmetric Killing Structures}, author={Frank Klinker}, journal={Communications in Mathematical Physics}, year={2005}, volume={255}, pages={419-467} }

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…

## 15 Citations

Generalized symmetry superalgebras

- Mathematics
- 2018

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions.…

Killing Vector Fields and Superharmonic Field Theories

- Mathematics
- 2013

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high…

Conformal symmetry superalgebras

- Mathematics
- 2013

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal…

Rigidity of Killing-Yano and conformal Killing-Yano superalgebras

- Mathematics
- 2017

Symmetry algebras of Killing vector fields and conformal Killing vectors fields can be extended to Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds. By defining…

Superconformal quantum field theory in curved spacetime

- Mathematics, Physics
- 2013

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor…

Twistor spinors and extended conformal superalgebras

- MathematicsJournal of Geometry and Physics
- 2020

Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension

- Mathematics
- 2014

A bstractWe consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed two-form that is invariant…

Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\&$ Odd Killing Vectors Fields

- Mathematics
- 2020

We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian…

The Torsion of Spinor Connections and Related Structures

- Mathematics
- 2006

In this text we introduce the torsion of spinor connections. In terms of the tor- sion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type…

## References

SHOWING 1-10 OF 42 REFERENCES

A Global Theory of Supermanifolds

- Mathematics
- 1980

A mathematically rigorous definition of a global supermanifold is given. This forms an appropriate model for a global version of superspace, and a class of functions is defined which corresponds to…

Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras

- Mathematics
- 1986

A new approach to superdifferentiable functions of Grassmann variables is developed, which avoids ambiguities in odd derivatives. This is used to give an improved definition of supermanifold over a…

A new maximally supersymmetric background of IIB superstring theory

- Mathematics, Physics
- 2002

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the…

Breaking the M-waves

- Mathematics
- 1999

We present a systematic attempt at classification of supersymmetric M-theory vacua with zero flux; that is, eleven-dimensional lorentzian manifolds with vanishing Ricci curvature and admitting…

Introduction to the Theory of Supermanifolds

- Mathematics
- 1980

CONTENTSIntroduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace §…

Instantons and the monopole-like equations in eight dimensions

- Mathematics
- 2000

We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies Spin(7) and SU(4). By mimicing the Seiberg-Witten theory in four…