High Energy Theory Seminar

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 modied 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, O, we consider the anomalous dimensions of the double-trace operators. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions. Non-renormalizable AdS interactions lead to violations of the bound at large values of double trace dimension. We also consider the case that these interactions are generated by integrating out a heavy scalar in AdS. We show that the presence of the heavy field unitarizes the growth in the anomalous dimensions, and leads to a resonance-like behavior. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from a certain limit of the anomalous dimensions of double-trace operators.