Effective conformal theory and the flat-space limit of AdS

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/ N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, , we consider the anomalous dimensions, γ ( n , l ), of the double-trace operators of the form . Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of | γ ( n , l )|