A converse Hawking-Unruh effect and \(dS^2\) correspondence (Q1424266)

This interesting work deals with several topics of local quantum field theory in de Sitter spacetime with dimension \(d\) establishing relevant results. In particular, the existence of a sort of ``converse to the Hawking-Unruh effect'' is investigated in the following sense. 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, the existence of observers that feel to be in a ground state (i.e. particle evolutions with positive generator) is studied. In fact, it is found that such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables. Afterwards the authors characterize the local conformal nets on \(dS^d\). Only in this case the above-cited positive energy evolutions have a complete geometrical meaning. Each net is found to have a unique maximal expected conformal subnet, where evolutions are geometrical. Finally attention is focused on the two-dimensional case where further interesting results are found. In particular, a holographic one-to-one correspondence between local nets \({\mathcal A}\) on \(dS^2\) and local conformal non-isotonic families (pseudonets) \({\mathcal B} \) on \(S^1\) is constructed. From the abstract: ``The pseudonet \({\mathcal B}\) gives rise to two local conformal nets \({\mathcal B}_\pm \) on \(S^1\), that correspond to the \( \mathfrak{H}_\pm \) 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 \(\mathfrak{H}_\pm\) have positive energy and the translations on \(\mathfrak{H}_\mp\) are trivial. This is the case iff the one-parameter unitary group implementing rotations on \(dS^2\) has positive/negative generator''.