Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries

Abstract

In the context of a canonical quantization of general relativity, one can deform the loop gravity phase space on a graph by replacing the T*SU(2) phase space attached to each edge by SL(2,C) seen as a phase space. This deformation is supposed to encode the presence of a non-zero cosmological constant. Here we show how to parametrize this phase space in terms of spinor variables, thus obtaining deformed spinor networks for loop gravity, with a deformed action of the gauge group SU(2) at the vertices. These are to be formally interpreted as the generalization of loop gravity twisted geometries to a hyperbolic curvature.

15 pages, 4 figures

References in corpus (3)

• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter
• Revisiting the Simplicity Constraints and Coherent Intertwiners

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