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arXiv · 2012.12622

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

Eugenia Colafranceschi·Daniele Oriti
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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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Eugenia Colafranceschi, Daniele Oriti. 2020-12-23. Quantum gravity states, entanglement graphs and second-quantized tensor networks. https://doi.org/10.1007/jhep07(2021)052

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