Seminarium Teorii Względności i Grawitacji

Many approaches to quantum gravity introduce a discretization of theunderlying manifold as an uv cutoff in order to obtain well defined models.Typically such a discretization leads however to a breaking of diffeomorphism symmetry. This represents a severe problem for lattice approaches to quantum gravity as diffeomorphism symmetry is deeply intertwined with the dynamics of general relativity. Perfect actions, which can be constructed by a renormalization block transformation from the continuum, might remedy the situation. These actions, although defined on the lattice, capture the continuum physics of the model, and hence should capture also the symmetries of the continuum. In this talk I will give an overview of the situation and describe recent progress.