Emergence of gravity from quantum field theory in triangulated spacetime and the QFT vector model

Abstract

We formulate quantum field theory in triangulated spacetime using compositional quantum field theory and tensor network methods. We show that gravitational interactions emerge as a low-energy effective phenomenon in this framework. For concrete calculations we use free massive scalar field theory in two-dimensional Lorentzian spacetime, but the results generalize to other models and higher dimensions. Finally, our results lead us to propose a new approach to the unification of quantum field theory with gravity, the QFT vector model, which combines insights and techniques from various current approaches to quantum gravity such as causal dynamical triangulations, random tensor models, group field theory, emergent gravity and holography.