Discrete gravity as a topological field theory with light-like curvature defects

Abstract

I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding null surfaces, which represent a system of curvature defects propagating at the speed of light. The underlying action is local and it is studied in both its Lagrangian and Hamiltonian formulation. The canonically conjugate variables on the null surfaces are a spinor and a spinor-valued two-surface density, which are coupled to a topological field theory for the Lorentz connection in the bulk. I discuss the relevance of the model for non-perturbative approaches to quantum gravity, such as loop quantum gravity, where similar variables have recently appeared as well.

52 pages, one figure, one table, v2: published version with extended conclusion

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• LQG vertex with finite Immirzi parameter
• Flipped spinfoam vertex and loop gravity
• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
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• Quantum Reference Frames at the Boundary of Spacetime
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• Corner symmetry and quantum geometry
• General Relativity with Local Space-time Defects
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Twistor representation of Jackiw-Teitelboim gravity
• Evidence for Planck Luminosity Bound in Quantum Gravity