Localized states in global AdS space

Abstract

We construct both local states and scattering states with finite energy in global AdS by inserting properly regularized operators in the CFT of arbitrary conformal dimension (Δ) at an instant of time. We give the state fixed angular momentum (l) by integrating the result over a sphere with appropriate spherical harmonics. The energy of the states and their angular resolution are computed with CFT operator methods and are independent of having an AdS interpretation. In the semiclassical limit of large conformal dimension 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 allows us to place a particle in any desired geodesic. For radial geodesics, we show that the amplitude to produce the desired state can be thought of as a regularized tunneling amplitude from the boundary to the radial turning point of the radial geodesic, while for other geodesics we argue that the insertion is at the outermost radial turning point of the corresponding geodesic.