# Charged conformal Killing spinors

## Abstract

We study the twistor equation on pseudo-Riemannian Spin{sup c}-manifolds whose solutions we call charged conformal Killing spinors (CCKSs). We derive several integrability conditions for the existence of CCKS and study their relations to spinor bilinears. A construction principle for Lorentzian manifolds admitting CCKS with nontrivial charge starting from CR-geometry is presented. We obtain a partial classification result in the Lorentzian case under the additional assumption that the associated Dirac current is normal conformal and complete the classification of manifolds admitting CCKS in all dimensions and signatures ≤5 which has recently been initiated in the study of supersymmetric field theories on curved space.

- Authors:

- Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, Room 1.310, D12489 Berlin (Germany)

- Publication Date:

- OSTI Identifier:
- 22403092

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; SPIN; SPINORS; SUPERSYMMETRY

### Citation Formats

```
Lischewski, Andree, E-mail: lischews@mathematik.hu-berlin.de.
```*Charged conformal Killing spinors*. United States: N. p., 2015.
Web. doi:10.1063/1.4906069.

```
Lischewski, Andree, E-mail: lischews@mathematik.hu-berlin.de.
```*Charged conformal Killing spinors*. United States. doi:10.1063/1.4906069.

```
Lischewski, Andree, E-mail: lischews@mathematik.hu-berlin.de. Thu .
"Charged conformal Killing spinors". United States.
doi:10.1063/1.4906069.
```

```
@article{osti_22403092,
```

title = {Charged conformal Killing spinors},

author = {Lischewski, Andree, E-mail: lischews@mathematik.hu-berlin.de},

abstractNote = {We study the twistor equation on pseudo-Riemannian Spin{sup c}-manifolds whose solutions we call charged conformal Killing spinors (CCKSs). We derive several integrability conditions for the existence of CCKS and study their relations to spinor bilinears. A construction principle for Lorentzian manifolds admitting CCKS with nontrivial charge starting from CR-geometry is presented. We obtain a partial classification result in the Lorentzian case under the additional assumption that the associated Dirac current is normal conformal and complete the classification of manifolds admitting CCKS in all dimensions and signatures ≤5 which has recently been initiated in the study of supersymmetric field theories on curved space.},

doi = {10.1063/1.4906069},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 56,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}

DOI: 10.1063/1.4906069

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