  We study \kk spectrum of type IIB string theory compactified on $AdS_5 \times
T^{nn'}$ in the context of $AdS/CFT$ correspondence. We examine some of the
modes of the complexified 2 form potential as an example and show that for the
states at the bottom of the \kk tower the corresponding $d=4$ boundary field
operators have rational conformal dimensions. The masses of some of the
fermionic modes in the bottom of each tower as functions of the $R$ charge in
the boundary conformal theory are also rational. Furthermore the modes in the
bottom of the towers originating from $q$ forms on $T^{11}$ can be put in
correspondence with the BRS cohomology classes of the $c=1$ non critical string
theory with ghost number $q$. However, a more detailed investigation is called
for, to clarify further the relation of this supergravity background with the
$c=1$ strings.
