Conformal Triality of de Sitter, Minkowski and Anti-de Sitter Spaces
Abstract
Description
We describe how conformal Minkowski, dS- and AdS-spaces can be united into a single submanifold [N] of RP^5. It is the set of generators of the null cone in M^{2,4}. Conformal transformations on the Mink-, dS- and AdS-spaces are induced by O(2,4) linear transformations on M^{2,4}. We also describe how Weyl transformations and conformal transformations can be resulted in on [N]. In such a picture we give a description of how the conformal Mink-, dS- and AdS-spaces as well as [N] are mapped from one to another by conformal maps. This implies that a CFT in one space can be translated into a CFT in another. As a consequence, the AdS/CFT-correspondence should be extended.
Talk on the XXIII International Conference of Differential Geometric Methods in Theoretical Physics, Chern Institute of Mathematics (former Nankai Institute of Mathematics), August 20--26, 2005. To appear in the proceedings, published by World Scientific. Plain LaTeX, 10 pages, no figures
Talk on the XXIII International Conference of Differential Geometric Methods in Theoretical Physics, Chern Institute of Mathematics (former Nankai Institute of Mathematics), August 20--26, 2005. To appear in the proceedings, published by World Scientific. Plain LaTeX, 10 pages, no figures