Twistorial phase space for complex Ashtekar variables

Abstract

We generalise the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group SL(2,C). We show that the phase space for complex valued Ashtekar variables on a spinnetwork graph can be decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.

18 pages, to appear in: Class. Quantum Grav

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Cited by in corpus (21)

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• Edge modes of gravity. Part III. Corner simplicity constraints
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• The twistorial structure of loop-gravity transition amplitudes
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Twistor Networks and Covariant Twisted Geometries
• Linking loop quantum gravity quantization ambiguities with phenomenology
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Null twisted geometries
• Twisted geometries, twistors and conformal transformations
• A note on the secondary simplicity constraints in loop quantum gravity
• Conformal boundary conditions, loop gravity and the continuum
• Discrete gravity as a topological field theory with light-like curvature defects
• Timelike twisted geometries
• Spinfoams: Foundations
• A one-dimensional action for simplicial gravity in three dimensions
• Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations
• Loop quantum gravity, twistors, and some perspectives on the problem of time
• An octahedron of complex null rays, and conformal symmetry breaking