  This paper studies a special class of states for the dual conformal field
theories associated with supersymmetric $AdS_5\times X$ compactifications,
where $X$ is a Sasaki-Einstein manifold with additional $U(1)$ symmetries.
Under appropriate circumstances, it is found that elements of the chiral ring
that maximize the additional $U(1)$ charge at fixed R-charge are in one to one
correspondence with multitraces of a single composite field. This is also
equivalent to Schur functions of the composite field. It is argued that in the
formal zero coupling limit that these dual field theories have, the different
Schur functions are orthogonal. Together with large $N$ counting arguments, one
predicts that various extremal three point functions are identical to those of
${\cal N}=4 $ SYM, except for a single normalization factor, which can be
argued to be related to the R-charge of the composite word. The leading and
subleading terms in $1/N$ are consistent with a system of free fermions for a
generalized oscillator algebra. One can further test this conjecture by
constructing coherent states for the generalized oscillator algebra that can be
interpreted as branes exploring a subset of the moduli space of the field
theory and use these to compute the effective K\"ahler potential on this subset
of the moduli space.
