Towards the map of quantum gravity

Understand

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics.

• In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations, Ho\v{r}ava-Lifshitz gravity, Asymptotic Safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed.
• The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincar\'{e} algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity.
• We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity.