Quantum gravity states, entanglement graphs and second-quantized tensor networks

• URL: http://arxiv.org/abs/2012.12622v3
• Date: Sat, 17 Jul 2021 08:25:57 GMT
• Title: Quantum gravity states, entanglement graphs and second-quantized tensor networks
• Authors: Eugenia Colafranceschi, Daniele Oriti
• Abstract summary: In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation in terms of graphs and simplicial complexes. We devote special attention to the implementation and consequences of the label independence of the graphs/networks, corresponding to the indistinguishability of the space quanta and representing a discrete counterpart of the diffeomorphism invariance of a consistent quantum gravity formalism. We also outline a relational setting to recover distinguishability of graph/network vertices at an effective and physical level, in a partial semi-classical limit of the theory.

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