TL;DR
This paper extends the Lie derivative concept to Lorentz tensors, introducing the Lie-Lorentz derivative, which plays a key role in supersymmetry transformations and supergravity field symmetries.
Contribution
It defines the Lie-Lorentz derivative for all Lorentz tensors and explores its application in supersymmetry algebra calculations.
Findings
Lie-Lorentz derivative generalizes Lie derivative for Lorentz tensors
It vanishes for Vielbeins, simplifying calculations
Enhances understanding of isometries in supergravity
Abstract
The definition of ``Lie derivative'' of spinors with respect to Killing vectors is extended to all kinds of Lorentz tensors. This Lie-Lorentz derivative appears naturally in the commutator of two supersymmetry transformations generated by Killing spinors and vanishes for Vielbeins. It can be identified as the generator of the action of isometries on supergravity fields and its use for the calculation of supersymmetry algebras is revised and extended.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.