Generating functional for gravitational null initial data

Abstract

A field theory on a three-dimensional manifold is introduced, whose field equations are the constraint equations for general relativity on a three-dimensional null hypersurface. The underlying boundary action consists of two copies of the dressed Chern-Simons term for self-dual Ashtekar variables, a kinetic term for the null flag at the boundary plus additional junction conditions for the spin coefficients across the interface. In fact, there is a doubling of the field content, because the null hypersurface will be considered as an internal boundary between two adjacent slabs of spacetime. The paper concludes with a proposal for a construction of the gravitational transition amplitudes in the bulk via the auxiliary boundary field theory alone, namely by gluing amplitudes for edge states across two-dimensional corners, thus providing a proposal for a quasi-local realisation of the holographic principle at the light front.

arXiv comment28 pages

References in corpus (30)

• The holographic principle
• Soft Hair on Black Holes
• The Spin Foam Approach to Quantum Gravity
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• BMS charge algebra
• Local subsystems in gauge theory and gravity
• Superrotation Charge and Supertranslation Hair on Black Holes
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Isolated Horizons: A Generalization of Black Hole Mechanics
• Soft Heisenberg hair on black holes in three dimensions
• Edge states in Gravity and Black Hole Physics
• Symmetries and charges of general relativity at null boundaries
• General boundary quantum field theory: Foundations and probability interpretation
• Fundamental theorem on gauge fixing at the action level
• New boundary variables for classical and quantum gravity on a null surface
• The loop gravity string
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Complex Ashtekar variables and reality conditions for Holst's action
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• 3D holography: from discretum to continuum
• Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• 2+1D Loop Quantum Gravity on the Edge
• Sachs' free data in real connection variables
• Conformal boundary conditions, loop gravity and the continuum
• Discrete gravity as a topological field theory with light-like curvature defects
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• The Poisson brackets of free null initial data for vacuum general relativity
• Holographic description of boundary gravitons in (3+1) dimensions

Cited by in corpus (12)

• Boundary effects in General Relativity with tetrad variables
• T-Witts from the horizon
• A note on dual gravitational charges
• Null infinity as an open Hamiltonian system
• Quantum Null Geometry and Gravity
• Kinematical Gravitational Charge Algebra
• Null Infinity and Horizons: A New Approach to Fluxes and Charges
• Gravitational $SL(2,\mathbb{R})$ Algebra on the Light Cone
• Covariant Momentum Map Thermodynamics for Parametrized Field Theories
• Twistor representation of Jackiw-Teitelboim gravity
• Quantum Area Fluctuations from Gravitational Phase Space
• Deformed Heisenberg charges in three-dimensional gravity