Projective Coordinates and Projective Space Limit
arXiv:0707.0326 · doi:10.1016/j.nuclphysb.2008.02.004
Abstract
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.
16 pages, v2: modified the section 2.1 clarifying the difference from IW contraction, added notes & references, version to appear in Nuclear Physics B
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