Coset for Hopf fibration and Squashing

Details Coset for Hopf fibration and Squashing Coset for Hopf fibration and Squashing

2009-06-05

arxiv.org/abs/0906.1025v2

Class.Quant.Grav.26:225007,2009

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, accepted for publication in Class. Quant. Gravity

Scientific paper

10.1088/0264-9381/26/22/225007

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.

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