A Converse HawkingUnruh Effect and dS2/CFT Correspondence
Abstract
Given a local quantum field theory net A on the de Sitter spacetime dS^d, where geodesic observers are thermalized at GibbonsHawking 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^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 twodimensional case, we construct a holographic onetoone correspondence between local nets A on dS^2 and local conformal nonisotonic 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 oneparameter unitary group implementing rotations on dS^2 has positive/negative generator.
 Publication:

Annales Henri Poincaré
 Pub Date:
 December 2003
 DOI:
 10.1007/s000230030159z
 arXiv:
 arXiv:grqc/0212025
 Bibcode:
 2003AnHP....4.1169G
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Operator Algebras
 EPrint:
 The title has changed. 38 pages, figures. To appear on Annales H. Poincare'