Corner Symmetry and Quantum Geometry

Freidel L, Geiller M, Wieland W (2023)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2023

Publisher: Springer

Edited Volumes: Handbook of Quantum Gravity

City/Town: Singapore

DOI: 10.1007/978-981-19-3079-9_107-1

Abstract

By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called corners. The presence of non-trivial corner symmetries associated with any entangling cut provides stringent constraints on the theory’s mathematical structure and a guide through quantization. This report reviews new and recent results for non-perturbative quantum gravity, which are natural consequences of this structure. First, we establish that the corner symmetry derived from the gauge principle encodes quantum entanglement across internal boundaries. We also explain how the quantum representation of the corner symmetry algebra provides us with a notion of quantum geometry. We then focus our discussion on the first-order formulation of gravity and show how many results obtained in the continuum connect naturally with the previous results in loop quantum gravity. In particular, we show that it is possible to get, purely from quantization and without discretization, an area operator with discrete spectrum, which is covariant under local Lorentz symmetry. We emphasize that while loop gravity correctly captures some of the gravitational quantum numbers, it does not capture all of them, which points toward important directions for future developments. Finally, we discuss the understanding of the gravitational dynamics along null surfaces as a conservation of symmetry charges associated with a Carrollian fluid.

Authors with CRIS profile

Wolfgang Wieland Chair for Theoretical Physics III (Quantum Gravity)

Involved external institutions

Perimeter Institute for Theoretical Physics CA Canada (CA) École normale supérieure de Lyon (ENS) FR France (FR)

How to cite

APA:

Freidel, L., Geiller, M., & Wieland, W. (2023). Corner Symmetry and Quantum Geometry. In Cosimo Bambi, Leonardo Modesto, Ilya Shapiro (Eds.), Handbook of Quantum Gravity. Singapore: Springer.

MLA:

Freidel, Laurent, Marc Geiller, and Wolfgang Wieland. "Corner Symmetry and Quantum Geometry." Handbook of Quantum Gravity. Ed. Cosimo Bambi, Leonardo Modesto, Ilya Shapiro, Singapore: Springer, 2023.

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