Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless t...

We reformulate the self-dual Einstein equation as a trio of di erential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in in nite-dimensional group, which was shown by Park and Husain earlier. We also derive other eld theories including the 2D Higgs bundle equation. This formulation elucidates the relation among thos...

A number of background independent quantizations procedures have recently been employed in 4d nonperturbative quantum gravity. We investigate and illustrate these techniques and their relation in the context of a simple 2d topological theory. We discuss canonical quantization, loop or spin network states, path integral quantization over a discretization of the manifold, spin foam formulation, a...

This work is devoted to the recently introduced Einstein–Gauss–Bonnet gravity in four dimensions. theory can bypass Lovelock’s theorem and avoids Ostrogradsky instability. The integrated part of this GB term which gives rise a non-trivial contribution gravitational dynamics limit D→4. Our main interest explore class static, spherically symmetric compact objects made strange matter. It believed ...