  Scalar fields on the bulk side of AdS/CFT correspondence can be assigned
unconventional boundary conditions, related to the conventional one by Legendre
transform. One can further perform double trace deformations which relate the
two boundary conditions via renormalization group flow. Thinking of these
operators as $S$ and $T$ transformations, respectively, we explore the
$SL(2,{\bf R})$ family of models which naively emerges from repeatedly applying
these operations. Depending on the parameters, the effective masses vary and
can render the theory unstable. However, unlike in the $SL(2,{\bf Z})$
structure previously seen in the context of vector fields in $AdS_4$, some of
the features arising from this exercise, such as the vacuum susceptibility,
turns out to be scheme dependent. We explain how scheme independent physical
content can be extracted in spite of some degree of scheme dependence in
certain quantities.
