A converse Hawking-Unruh effect and dS2/CFT correspondence

Given a local quantum field theory net A on the de Sitter spacetime dS(d), 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 Hawking-Unruh 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(d). 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(2) and local conformal non-isotonic families (pseudonets) B+/- on S-1. The pseudonet B gives rise to two local conformal nets B+/- on S-1, 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(2) has positive/negative generator.