This could have gone in about 4 different forums, so I apologize if I picked the wrong one. I'm wondering if anyone can explain what (conformal) killing spinors are all about. All I can find is that they are sections of the spinor bundle of a spin manifold satisfying:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \nabla_\mu \epsilon = \lambda \gamma_\mu \epsilon [/tex]

where [itex]\nabla_\mu[/itex] is the spinor covariant derivative, [itex]\gamma_\mu[/itex] are the dirac matrices, and [itex]\lambda[/itex] is a constant. I've also seen something like this pair of equations used to define them:

[tex] \nabla_\mu \epsilon = \gamma_\mu \epsilon' [/tex]

[tex] \nabla_\mu \epsilon' = c R \gamma_\mu \epsilon [/tex]

where R is the scalar curvature and c is some specific constant, possibly depending on dimension, that I can't remember right now.

First of all, which equation is correct, and in the case of the second, which is the killing spinor? Second, how should I think about these geometrically? Where do these equations come from? I've come across these working on supersymmetry, and I'd like to know why they are important there. If anyone could try to explain some of this, or point me to some good sources, I'd really appreciate it.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Killing spinors

Loading...

Similar Threads - Killing spinors | Date |
---|---|

I Killing's vectors | Jun 29, 2017 |

A Question about Killing vector fields | Jul 26, 2016 |

Some questions about isometry | Oct 3, 2014 |

Why is there maximally 1/2 n(n+1) killing vectors? | Sep 24, 2014 |

4 component spinor isomorphic to S^7? | May 7, 2012 |

**Physics Forums - The Fusion of Science and Community**