  Non-chiral operators with positive anomalous dimensions can have interesting
applications to supersymmetric model building. Motivated by this, we develop a
new method for obtaining the anomalous dimensions of non-chiral double-trace
operators in N=1 superconformal field theories (SCFTs) with weakly-coupled AdS
duals. Via the Hamiltonian formulation of AdS/CFT, we show how to directly
compute the anomalous dimension as a bound state energy in the gravity dual.
This simplifies previous approaches based on the four-point function and the
OPE. We apply our method to a class of effective AdS5 supergravity models, and
we find that the binding energy can have either sign. If such models can be UV
completed, they will provide the first calculable examples of SCFTs with
positive anomalous dimensions.
