Establishing the Uniqueness of the Connection between SdS₅ and Conformally Invariant Relativistic Systems: A Group/Field Theoretical Approach

Adopting as working assumption that the conformal group O(4,2) of Minkowski space, being the largest symmetry group which respects its light cone structure, is the appropriate global symmetry underlying the description of relativistic systems, it is shown that AdS$_5$ uniquely emerges as the space on the boundary of which a corresponding relativistic field system should be accommodated. The basic mathematical tools employed for establishing this result are (a) Cartan's theory of spinors and (b) group contraction methods. Extending our considerations to supersymmetry it is demostrated how an $N$=1 SUSY YM field system can emerge as a broken version of an $N$=4 SUSY YM field system. An especially important feature of the presentation is the `unearthing' of seminal, independent from each other, works of I. Segal and of S. Fubini which give a purely field theoretical perspective on the intimate relation between conformally invariant relativistic field theories and AdS$_5$ including, in particular, the warping phenomenon.