A non-local way around the no-global-symmetries conjecture in quantum gravity?

The no-global-symmetries conjecture is central to the swampland program that delineates the boundary between effective field theories that can be obtained from a quantum theory of gravity to those that cannot. The conjecture states that virtual black-hole configurations in the path integral generate terms that violate all global symmetries in the effective action for matter. Because of its central role, it is crucial to understand limitations to the validity of this conjecture. In the context of the Lorentzian path integral over spacetime geometries, we explore whether virtual black-hole configurations can be suppressed dynamically. To that end, we work in a spherically symmetric setting and make use of horizon-detecting curvature invariants which vanish on the horizon. By constructing a non-local gravitational action from the inverse of such curvature invariants, we can achieve destructive interference of black-hole configurations in the path integral. Given that non-local gravitational actions appear generically as the result of integrating out matter degrees of freedom from a theory for quantum gravity and matter, our exemplary construction reinforces discussions about the role of non-locality in assessing arguably universal properties of quantum gravity within the framework of path integrals.