Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models

Understand

The universal coupling of matter and gravity is one of the most important features of general relativity.

• In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretisation.
• However extracting this mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories.
• Therefore, we introduce a simple 2D toy model for Yang--Mills coupled to spin foams, namely an Ising model coupled to so--called intertwiner models defined for $\text{SU}(2)_k$.