Lattice Quantum Gravity: EDT and CDT

This chapter contains an overview of the use of so-called Euclidean dynamical triangulations (EDT) and causal dynamical triangulations (CDT) as lattice regularizations of quantum gravity. The lattice regularizations have been very successful in the case of two-dimensional quantum gravity, where the lattice theories indeed provide regularizations of continuum well-defined quantum gravity theories. In four-dimensional spacetime the Einstein–Hilbert action leads to a theory of gravity which is not renormalizable as a perturbative quantum theory around flat spacetime. It is discussed how lattice gravity in the form of EDT or CDT can be used to search for a non-perturbative UV fixed point of the lattice renormalization group in the spirit of asymptotic safety. In this way it might be possible to define a quantum theory of gravity also at length scales smaller than the Planck length.