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

TL;DR

This paper explores a novel converse to the Hawking-Unruh effect in de Sitter spacetime, characterizing local quantum field theories and establishing a holographic correspondence with conformal nets on S^1, revealing geometric and spectral conditions for positive energy evolutions.

Contribution

It introduces a new perspective on the Hawking-Unruh effect by identifying positive energy evolutions with geometric meaning and constructs a holographic duality between de Sitter nets and conformal pseudonets on the circle.

Findings

Positive energy evolutions map localized observables into localized observables.

Unique maximal conformal subnet exists where evolutions are geometric.

Holographic correspondence relates de Sitter nets to conformal pseudonets on S^1.

Abstract

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.