Title: Symmetries of coset spaces and Kaluza-Klein supergravity
Abstract: Known theorems about the isometry group of a general coset space GH are reviewed. The Killing vectors on GH are explicitly constructed. Rescalings of the coset vielbeins are discussed, and a simple criterion to find which rescalings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the rescaled vielbeins and the group structure constants is derived. These results have useful applications in Kaluza-Klein theories. As an example, the round and the squashed seven-spheres that have been used to compactify d = 11 supergravity are discussed, and it is shown that they can be identified with two appropriately rescaled coset spaces SO(5)SO(3).
Publication Year: 1984
Publication Date: 1984-10-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 69
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot