Complex saddles and Euclidean wormholes in the Lorentzian path integral

A bstract We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms a 3-form flux, which include Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using with help Picard-Lefschetz theory. The number nature is shown to qualitatively change presence bilocal operator that could arise, example, as result considering higher-topology transitions. also analyze stability wormhole picture, where we find it represents perturbatively stable saddle gravitational integral. This calls into question ultimate fate such solutions an ultraviolet-complete theory quantum gravity.