Projective Coordinates and Projective Space Limit

Details Projective Coordinates and Projective Space Limit Projective Coordinates and Projective Space Limit

2007-07-03

arxiv.org/abs/0707.0326v2

Nucl.Phys.B798:310-322,2008

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, v2: modified the section 2.1 clarifying the difference from IW contraction, added notes & references, version to app

Scientific paper

10.1016/j.nuclphysb.2008.02.004

The "projective lightcone limit" has been proposed as an alternative holographic dual of an AdS space. It is a new type of group contraction for a coset G/H preserving the isometry group G but changing H. In contrast to the usual group contraction, which changes G preserving the spacetime dimension, it reduces the dimensions of the spacetime on which G is realized. The obtained space is a projective space on which the isometry is realized as a linear fractional transformation. We generalize and apply this limiting procedure to the "Hopf reduction" and obtain (n-1)-dimensional complex projective space from (2n-1)-dimensional sphere preserving SU(n) symmetry.

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