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.
Highlights
Seems to be played by the quantum phenomenon of entanglement
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
In this paper we detail a correspondence between the quantum states of the quantum gravity formalism of group field theory (GFT) [10] and the quantum information language of tensor networks (TN) [11,12,13,14], which defines a promising framework to perform both tasks, thanks to the importing of quantum information techniques in a proper quantum gravity setting
Summary
A GFT is a field theory whose domain is given by (d copies of) a group manifold and characterized by combinatorially non-local interactions. Additional conditions are imposed, normally at the level of the GFT dynamics, in 4d gravitational models, where the group is taken to be SU(2) or SL(2, C) or Spin(4), to ensure the proper geometric interpretation of the GFT quanta and the discrete structures they form. These geometric aspects, while crucial for the interpretation of the formalism in a quantum gravity context, are not directly relevant for our present purposes. The GFT Fock space is constructed starting from a vacuum state |0 annihilated by φ(gx), with the fundamental simplices created by the action of φ†(gx) on |0
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