A Converse Hawking-Unruh Effect and $dS^2$/CFT Correspondance

Daniele Guido, Roberto Longo
December 05, 2002
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.