From lattice BF gauge theory to area-angle Regge calculus

Understand

We consider Riemannian 4d BF lattice gauge theory, on a triangulation of spacetime.

• Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3d and 4d dihedral angles, are identified.
• The parallel transport conditions are taken care of to ensure a consistent gluing of simplices.
• We show that these gluing relations, together with the simplicity constraints, contain the constraints of area-angle Regge calculus in a simple way, via the group structure of the underlying BF gauge theory.