A Converse Hawking-Unruh Effect and dS2/CFT Correspondence

Given a local quantum field theory net $ mathcal{A} $ on the de Sitter spacetime dS ^d ,where geodesic observers are thermalized at Gibbons-Hawking temperature, we lookfor observers that feel to be in a ground state, i.e., particle evolutions with positivegenerator, providing a sort of converse to the Hawking-Unruh effect. Such positiveenergy evolutions always exist as noncommutative flows, but have only a partialgeometric meaning, yet they map localized observables into localized observables.We characterize the local conformal nets on dS ^d . Only in this case our positiveenergy evolutions have a complete geometrical meaning. We show that each nethas a unique maximal expected conformal subnet, where our evolutions are thusgeometrical.In the two-dimensional case, we construct a holographic one-to-one correspondencebetween local nets $ mathcal{A} $ on dS ² and local conformal non-isotonic families(pseudonets) $ mathcal{B} $ on S ¹. The pseudonet $ mathcal{B} $ gives rise to two local conformal nets$ mathcal{B}_pm $ on S ¹, that correspond to the $ frak{H}_pm $ horizon components of $ mathcal{A} $, and to the chiralcomponents of the maximal conformal subnet of $ mathcal{A} $. In particular, $ mathcal{A} $ is holographicallyreconstructed by a single horizon component, namely the pseudonet is a net,iff the translations on $ frak{H}_pm $ have positive energy and the translations on $ frak{H}_mp $ aretrivial. This is the case iff the one-parameter unitary group implementing rotationson dS ² has positive/negative generator. Communicated by Klaus Fredenhagen submitted 07/02/03, accepted: 07/07/03