Pre-holography

We construct a symplectic isomorphism h from classical Klein Gordon solutions of mass m on (d+1)-dimensional Lorentzian anti de Sitter space (equipped with the usual symplectic form) to a certain symplectic space of functions on its conformal boundary (only) for all integer and half-integer Δ (=(d)/(2)+(1)/(2)(d²+4m²)^1/2). h induces a large family of new examples of Rehren’s algebraic holography in which the net of local quantum Klein Gordon algebras in AdS is seen to map to a suitably defined net of local algebras for the (generalized free) scalar conformal field with anomalous dimension Δ on d-dimensional Minkowski space (the AdS boundary). Relatedly, we show for these models that Bertola et al.’s boundary-limit holography becomes a quantum duality (only) if the test functions for boundary Wightman distributions are restricted in a particular way.