Würzburg Seminar on Quantum Field Theory and Gravity

In this talk, I will explore the utility of tensor networks in studying gravity through holography. I will introduce a time-independent model of AdS/CFT that serves as an infinite-dimensional analog of the HaPPY code. This model features decaying two-point correlation functions and fractal structures, capturing the conformal field theory (CFT) nature at the boundary. Building on this foundation, I will present a novel spacetime tensor network. This network is constructed as a lattice model with discretized spacetime taken to the continuum limit in both spatial and temporal directions. This new framework is analyzed as a series of stabilizer codes, each defined within specific Hilbert spaces and interconnected through isometric maps. The construction is a genuine spacetime quantum error-correcting code. The model integrates U(1) time evolution, leading to the emergence of a Hubeny-Rangamani-Takayanagi (HRT) surface. The tensor network successfully capture the essential features of spacetime, including lightcones and causality, thereby revealing a genuine emergent bulk geometry.