Curvature in spinfoams

Understand

We consider spinfoam quantum gravity.

• We show in a simple case that the amplitude projects over a nontrivial (curved) classical geometry.
• This suggests that, at least for spinfoams without bubbles and for large values of the boundary spins, the amplitude takes the form of a path integral over Regge metrics, thus enforcing discrete Einstein equations in the classical limit.
• The result relies crucially on a new interpretation of the semiclassical limit for the amplitudes truncated to a fixed 2-complex.