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We consider a scalar field theory in AdS_{d+1}, and introduce a formalism onsurfaces at equal values of the radial coordinate. In particular, we define thecorresponding conjugate momentum. We compute the Noether currents forisometries in the bulk, and perform the asymptotic limit on the correspondingcharges. We then introduce Poisson brackets at the border, and show that theasymptotic values of the bulk scalar field and the conjugate momentum transformas conformal fields of scaling dimensions \Delta_{-} and \Delta_{+},respectively, where \Delta_{\pm} are the standard parameters giving theasymptotic behavior of the scalar field in AdS. Then we consider the case d=2,where we obtain two copies of the Virasoro algebra, with vanishing centralcharge at the classical level. An AdS_3/CFT_2 prescription, giving thecommutators of the boundary CFT in terms of the Poisson brackets at the border,arises in a natural way. We find that the boundary CFT is similar to ageneralized ghost system. We introduce two different ground states, and thencompute the normal ordering constants and quantum central charges, which dependon the mass of the scalar field and the AdS radius. We discuss certainimplications of the results.

A Note on Scalar Field Theory in AdS_3/CFT_2