Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries

Understand

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.