Stability and boundedness in AdS/CFT with double trace deformations

Understand

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.