Würzburg Seminar on Quantum Field Theory and Gravity

In this talk, I will introduce a general class of tensor networks that model discrete holographic dualities. This class of networks contains all usual examples of holographic tensor networks, but is much larger. In particular, in the generic case, the boundary theory lives on a fractal. For a suitable set of regions, the networks obey a Ryu--Takayanagi formula and the areas of Ryu--Takayanagi surfaces are controlled by the Hausdorff dimension of the boundary, in a way that consistently generalizes the behavior of holographic entanglement entropy in integer dimensions to the non-integer case. This construction opens a path towards a more fundamental understanding of holography on discrete spaces, and hints at a notion of conformal field theory and holography on fractals. The talk is based on a collaboration with Matilde Marcolli and Sarthak Parikh (arXiv:2202.01788).