compactification of IIB supergravity on $S^5$[@doub2]. However, these degrees of freedom could be gauged away everywhere but in the boundary of $adS_5$. The anti-de Sitter group $SO(d-1,2)$ coincides with the conformal group in one dimension lower. It follows that the singleton field theory is a superconformal field theory. Similar remarks apply for the M-theory branes. The supergravity solution describing a membrane $M2$ (a fivebrane $M5$) is mapped to a spacetime which is locally isometric to $adS_4 \xx S^7$ ($adS_7 \xx S^4$), and furthermore the worldvolume fields of $M2$ ($M5$) are the same as the ones in the singleton (doubleton) multiplet of $adS_4$ ($adS_7$). (From now on, we shall not distinguish between singletons and doubletons. We shall call both singletons.[^2]) These facts have led to an association of branes to singletons[@m2; @NST; @m5; @f1; @KSKS; @BPS2].

A puzzle arises, however, when one considers multiple coincident branes. In the case of $D$-branes there are new massless states that arise from strings that become massless when one moves the branes on top of each other. This leads to enhanced gauge symmetry [@witten1]. In particular, the worldvolume theory of $N$ coincident $D3$ branes is an $SU(N)$ $\cn=4$ SYM theory. The shift transformation though does 