Abstract.
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 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 $ \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 chiral components of the maximal conformal subnet of $ \mathcal{A} $. In particular, $ \mathcal{A} $ is holographically reconstructed 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 $ are trivial. This is the case iff the one-parameter unitary group implementing rotations on dS 2 has positive/negative generator.
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Communicated by Klaus Fredenhagen
submitted 07/02/03, accepted: 07/07/03
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Guido, D., Longo, R. A Converse Hawking-Unruh Effect and dS2/CFT Correspondence . Ann. Henri Poincaré 4, 1169–1218 (2003). https://doi.org/10.1007/s00023-003-0159-z
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DOI: https://doi.org/10.1007/s00023-003-0159-z