  The bulk phase shift, related to a CFT four-point function, describes
two-to-two scattering at fixed impact parameter in the dual AdS spacetime. We
describe its properties for a generic CFT and then focus on large $N$ CFTs with
classical bulk duals. We compute the bulk phase shift for vector operators
using Regge theory. We use causality and unitarity to put bounds on the bulk
phase shift. The resulting constraints bound three-point functions of two
vector operators and the stress tensor in terms of the gap of the theory.
Similar bounds should hold for any spinning operator in a CFT. Holographically
this implies that in a classical gravitational theory any non-minimal coupling
to the graviton, as well as any other particle with spin greater than or equal
to two, is suppressed by the mass of higher spin particles.
