Symmetries of coset spaces and Kaluza-Klein supergravity

✍ Scribed by L Castellani; L.J Romans; N.P Warner

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 569 KB
• Volume: 157
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(84)90066-6

✦ Synopsis

Known theorems about the isometry group of a general coset space G/H are reviewed. The Killing vectors on G/H are explicitly constructed. Resealings of the coset vielbeins are discussed, and a simple criterion to find which resealings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the resealed 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 resealed coset spaces SO(5)/SO(3). sr 1984 Academic Press. Inc.