/cft Correspondence

Given a local quantum field theory net A on the de Sitter spacetime dS, where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e. particle evolutions with positive generator, providing a sort of converse to the HawkingUnruh effect. Such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables. We characterize the local conformal nets on dS. Only in this case our positive energy evolutions have a complete geometrical meaning. We show that each net has a unique maximal expected conformal subnet, where our evolutions are thus geometrical. In the two-dimensional case, we construct a holographic one-to-one correspondence between local nets A on dS and local conformal non-isotonic families (pseudonets) B on S. The pseudonet B gives rise to two local conformal nets B± on S, that correspond to the H± horizon components of A, and to the chiral components of the maximal conformal subnet of A. In particular, A is holographically reconstructed by a single horizon component, namely the pseudonet is a net, iff the translations on H± have positive energy and the translations on H∓ are trivial. This is the case iff the one-parameter unitary group implementing rotations on dS has positive/negative generator.