An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
Quantum Corner Symmetry: Representations and Gluing
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abstract
The corner symmetry algebra organises the physical charges induced by gravity on codimension-$2$ corners of a manifold. In this letter, we initiate a study of the quantum properties of this group using as a toy model the corner symmetry group of two-dimensional gravity $\mathrm{SL}\left(2,\mathbb{R}\right)\ltimes \mathbb{R}^2$. We first describe the central extensions and how the quantum corner symmetry group arises and give the Casimirs. We then make use of one particular representation to discuss the gluing of corners, achieved by identifying the maximal commuting sub-algebra. This is a concrete implementation of the gravitational constraints at the quantum level.
fields
hep-th 2years
2026 2representative citing papers
Derives a thermal fluctuation formula for causal-diamond boundary area with a linear term of Verlinde-Zurek scaling interpreted as statistical evidence for discrete quanta of geometry.
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Quantization of Gravity on Null Hypersurfaces
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
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Quantum Geometry from Area Fluctuations
Derives a thermal fluctuation formula for causal-diamond boundary area with a linear term of Verlinde-Zurek scaling interpreted as statistical evidence for discrete quanta of geometry.