should carry UIRs of the anti-de Sitter group. Therefore, a necessary condition for the duality to work is that there are multiplets of the anti-de Sitter group that can carry the original degrees of freedom. This is a very non-trivial condition since from the point of view of classical relativity asymptotically flat spacetimes are different from asymptotically anti-de Sitter spacetimes. It is string theory that makes such a connection possible.

To make the discussion concrete consider the case of a Dirichlet three-brane ($D3$) in IIB string theory. The duality transformation maps the supergravity solution describing the $D3$ brane to a space which is locally isometric to $adS_5 \xx S^5$. In the limit of decoupling gravity one is left with the $D3$ worldvolume fields. For a single $D3$ brane the latter belong to a $U(1)$ $\cn=4$ super Yang-Mills (SYM) multiplet. For the duality to work there should exist a UIR of the $adS_5$ supergroup that contains precisely these fields. Indeed, it turns out that such a multiplet exists. It is the so-called doubleton multiplet of $adS_5$.[^1] The latter is the most fundamental multiplet of $adS_5$. All other UIRs can be constructed by a tensoring procedure[@doub1]. The doubleton multiplet appeared in the 