Localized states in global AdS space

We construct both local states and scattering states with finite energy in global AdS by inserting properlyregularized operators in the CFT of arbitrary conformal dimension (Δ) at an instant of time. We give thestate fixed angular momentum (ℓ) by integrating the result over a sphere with appropriate sphericalharmonics. The energy of the states and their angular resolution are computed with CFT operator methodsand are independent of having an AdS interpretation. In the semiclassical limit of large conformaldimension operators, these correspond to single particles localized within sub-AdS scales with width 1/√Δ in AdS units, whose subsequent evolution is controlled by bulk geodesics. Our construction allowsus to place a particle in any desired geodesic. For radial geodesics, we show that the amplitude to producethe desired state can be thought of as a regularized tunneling amplitude from the boundary to the radialturning point of the radial geodesic, while for other geodesics we argue that the insertion is at the outermostradial turning point of the corresponding geodesic.