Matter fields in triangle-hinge models

Understand

The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane.

• In a recent paper [arXiv:1503.08812] a new class of models are introduced that generate three-dimensional random volumes, where the Boltzmann weight of each configuration is given by the product of values assigned to the triangles and the hinges.
• These triangle-hinge models describe three-dimensional pure gravity and are characterized by semisimple associative algebras.
• In this paper, we introduce matter degrees of freedom to the models by coloring simplices in a way that they have local interactions.