From Coarse-Graining to Holography in Loop Quantum Gravity

Abstract

We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we integrating out physical degrees of freedom or gauge degrees of freedom? Focusing on how bulk spin network states for bounded regions of space are projected onto boundary states, we show that all possible boundary states can be recovered from bulk spin networks with a single vertex in the bulk and a single internal loop attached to it. This partial reconstruction of the bulk from the boundary leads us to the idea of realizing the Hamiltonian constraints at the quantum level as a gauge equivalence reducing arbitrary spin network states to one-loop bulk states. This proposal of "dynamics through coarse-graining" would lead to a one-to-one map between equivalence classes of physical states under gauge transformations and boundary states, thus defining holographic dynamics for loop quantum gravity.

6 pages; v2: added explicit examples of holographic dynamics with the BF case and an "area-preserving" dynamics

References in corpus (8)

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• Lorentz covariance of loop quantum gravity
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Cited by in corpus (8)

• Towards effective actions for the continuum limit of spin foams
• 2+1D Loop Quantum Gravity on the Edge
• Loop Quantum Gravity's Boundary Maps
• Holographic entanglement in spin network states: a focused review
• Loop Quantum Gravity and Quantum Information
• Curvature from multipartite entanglement in quantum gravity states
• Macroscopic observables from the comparison of local reference systems
• Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity