a Surface-Theoretic Quantum Gravity Model

A surface theoretic view of non-perturbative quantum gravity was studied some time ago based on 3 dimensional general relativity as a reformulation of the Ponzano-Regge model in Riemannian spacetime.¹ Since 3 dimensional general relativity has no local degrees of freedom, the Ponzano-Regge model is known to be a topological field theory called lattice BF theory in 3 dimensions. On the other hand, the 4 dimensional generalization made by Ooguri is known as lattice BF theory in 4 dimensions, also a topological field theory.² This Ooguri model similarly allows the surface theoretic view. However, since 4 dimensional general relativity contains local degrees of freedom, the Ooguri model is not a quantization of general relativity...