Projective Coordinates and Projective Space Limit
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.
Cite
@article{arxiv.0707.0326,
title = {Projective Coordinates and Projective Space Limit},
author = {Machiko Hatsuda and Kiyoshi Kamimura},
journal= {arXiv preprint arXiv:0707.0326},
year = {2008}
}
Comments
16 pages, v2: modified the section 2.1 clarifying the difference from IW contraction, added notes & references, version to appear in Nuclear Physics B