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

Abstract

We formulate quantum field theory in triangulated spacetimes using compositional quantum field theory and tensor network methods. We show that, in the case of free massive scalar field theory in two-dimensional Lorentzian spacetime, an effective gravitational action emerges from the quantum field theory amplitudes, similarly to Sakharov's induced gravity approach. The generalization to higher dimensions and other models is also discussed, but the details are left for future work. 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. The key idea behind the approach is that, if indeed matter QFT induces effective quantum gravitational amplitudes, then we may not need to include gravitational dynamics explicitly into the fundamental model in order to obtain a unified theory of quantum matter and gravity.