Holographic toy models for de Sitter spacetime
Creators: name: Niermann, Laura Charlotte
Publisher: name: Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
Year: 2024
Subjects: subject: dS/CFT
subject: holography
subject: Thompson's group T
subject: Unruh effect
subject: optimal cloning
subject: superposition
subject: Holografie
subject: Thompson's Gruppe T
subject: Unruh Effekt
subject: optimales Klonen
subject: Superposition
subject: Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik

description: Quantum information tools have yielded crucial insights into quantum gravity, particularly within the framework of anti-de Sitter spacetime, where the AdS/CFT correspondence is well-established. The assumption has intensified that this connection can be extended to a broader context of quantum gravity. Bridging the knowledge gap from anti-de Sitter to de Sitter spacetime has been a significant pursuit in recent decades. This thesis takes a step in advancing our comprehension of quantum gravity in the context of low-dimensional de Sitter spacetime using holography. To achieve this, we develop a holographic toy model to describe the dS/CFT correspondence. This model is defined as a tensor network associated with the tessellation of de Sitter spacetime, which is interpreted as a propagator from de Sitter’s past to its future boundary. Notably, the symmetry action on the boundaries of this holographic model is fully characterized using Thompson’s Group T; with this, we provide a dynamical toy model for the dS/CFT correspondence. By extending the holographic models to various curvatures of de Sitter, we establish a correlation between the curvature of spacetime and the quantum capacity of the channel defined by the tensor network, which is reminiscent of the Λ-N correspondence. Another key property of the holographic model is that it captures an isometric time evolution in expanding spacetime, which is in contrast to a unitary time evolution established in standard quantum mechanics. To relate the holographic model to the language of quantum mechanics, we define Hilbert spaces at the holographic boundaries and physical quantum states living in these Hilbert spaces. It is crucial to emphasize that the properties of tensors within the holographic model significantly influence the characteristics of permissible states and with that the model’s physical significance. Unlike in the anti-de Sitter case, using quantum error correction here only yields a trivial theory. To further motivate more concrete properties of the tensors, we investigate how a local observer experiences the expansion of de Sitter spacetime. For this, we suggest a de Sitter vacuum state with quantum fluctuations as a globally defined initial state of de Sitter spacetime. We derive how its evolution is perceived by a local observer who experiences proper acceleration due to the spacetimes expansion. We refer to this as an Unruh channel in de Sitter spacetime. The obtained channel exhibits properties of an optimal cloning channel, which establishes another connection between aspects of quantum information theory and the expansion of spacetime. One central principle that sets quantum physics apart from classical physics is quantum superposition. At the end of this thesis, we extend our studies of the Unruh effect to allow for the detector to be in a quantum superposition of trajectories. For this, we consider trajectories in a de Sitter static patch with a constant distance from one another and analyze the resulting state of the detector. We find that the state of the detector is not only a mixture of thermal states known from a well-defined trajectory, but we find interference terms between different trajectories in the excited state of the detector. These coherences can be associated with the properties of the particles absorbed by the detector.