Coset for Hopf fibration and squashing

2009/06/30 by Machiko Hatsuda, Shinya Tomizawa
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/26/22/225007

published as Class.Quant.Grav.26:225007,2009 · 19 pages, accepted for publication in Class. Quant. Gravity

arxiv created 2009/09/25 · openalex publication_date 2009/10/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and Z_k quotient which play essential roles in recent studies on the AdS4/CFT3. A general metric formula of Hopf fibrations for complex and quaternion cosets is presented. Squashing is given by a similarity transformation which changes the metric preserving the isometry symmetry of the projective space. On the other hand Z_k quotient is given as a lens space which changes the topology preserving the "local" metric.

Citations

• Horizons of coalescing black holes on the Eguchi–Hanson space
• A rotating Kaluza–Klein black hole with squashed horizons
• Supersymmetric black rings on Eguchi–Hanson space
• Selfdual strings and loop space Nahm equations
• Charged black holes in a rotating Gross–Perry–Sorkin monopole background
• Gauge symmetry and supersymmetry of multiple M2-branes