not depend on the number of $D3$ branes. So, by the same argument as before one expects to find the $SU(N)$ degrees of freedom in the $adS$ side. However, as we argued in footnote \[nonab\] it is rather unclear whether non-abelian singletons exist. So these degrees of freedom should appear in a more subtle way.

In a parallel development Maldacena[@malda] (for earlier related work see [@kleb]) conjectured that the large $N$ limit of $\cn=4$ $SU(N)$ SYM is described by IIB supergravity on $adS_5 \xx S^5$. This conjecture was further sharpened in [@GKP; @witten2], where a precise correspondence between the conformal field theory and the supergravity was proposed. In particular, it was shown that the chiral operators of $\cn=4$ $SU(N)$ SYM correspond to the Kaluza-Klein modes on $S^5$. This provides the resolution of the puzzle raised in the previous paragraph. Notice that the large $N$ limit is needed in our case in order to trust the spacetime picture. Similar remarks hold for the cases of $M2$ and $M5$. These developments have led to a series of papers [@toine]-[@rey].

Most of the recent papers were devoted to the study of $adS_4$, $adS_5$ and $adS_7$. However, in these cases the corresponding superconformal theories 