Quantum gravity with purely virtual particles from asymptotically local quantum field theory

We investigate the relationship between nonlocal and local quantum field theories, and search for a viable notion of “local limit” to relate the unitary models. In Euclidean space it is relatively easy to have nonlocal theories with well-behaved local limits. In Minkowski spacetime, instead, singular behaviors are generically expected. Relaxing some assumptions on the “form factors” considered in the literature, we identify a class of models that have regular local limits in Minkowski spacetime. We call the models “asymptotically local” quantum field theories (AL-QFTs) and show that their limits are theories with physical and purely virtual particles (PVPs). In the bubble diagram, the nonlocal deformation generates PVPs straightforwardly. In the triangle diagram, it does so possibly up to multi-threshold corrections, which may be adjusted by tuning the deformation itself. We also build an asymptotically local deformation of quantum gravity with purely virtual particles. AL-QFT can serve various purposes, such as suggesting innovative approaches to off-shell physics, providing an alternative formulation for theories with PVPs, or smoothing out nonanalytic behaviors. We discuss its inherent arbitrariness and the implications for renormalizability.