• DOI:10.1007/s00023-003-0159-z
• Corpus ID: 119151913

A Converse Hawking-Unruh Effect and dS2/CFT Correspondence

@article{Guido2003ACH,
  title={A Converse Hawking-Unruh Effect and dS2/CFT Correspondence
},
  author={Daniele Guido and Roberto Longo},
  journal={Annales Henri Poincar{\'e}},
  year={2003},
  volume={4},
  pages={1169-1218}
}

• D. Guido, R. Longo
• Published 5 December 2002
• Mathematics, Physics
• Annales Henri Poincaré

Abstract.
Given a local quantum field theory net $ \mathcal{A} $ on the de Sitter spacetime dSd,
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 dSd. 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 dS2 and local conformal non-isotonic families
(pseudonets) $ \mathcal{B} $ on S1. The pseudonet $ \mathcal{B} $ gives rise to two local conformal nets
$ \mathcal{B}_\pm $ on S1, 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 dS2 has positive/negative generator.