Coarse graining of spin net models: dynamics of intertwiners

Abstract

Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four-dimensional models. We consider here simplified analogue models, so called spin nets, that retain the main dynamical ingredient of spin foams, the simplicity constraints. For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model. © IOP Publishing and Deutsche Physikalische Gesellschaft.