Coarse graining flow of spin foam intertwiners

Understand

Simplicity constraints play a crucial role in the construction of spin foam models, yet their effective behaviour on larger scales is scarcely explored.

• In this article we introduce intertwiner and spin net models for the quantum group $\text{SU}(2)_k \times \text{SU}(2)_k$, which implement the simplicity constraints analogous to 4D Euclidean spin foam models, namely the Barrett-Crane (BC) and the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) model.
• These models are numerically coarse grained via tensor network renormalization, allowing us to trace the flow of simplicity constraints to larger scales.
• In order to perform these simulations we have substantially adapted tensor network algorithms, which we discuss in detail.