Complex Saddles and Euclidean Wormholes in the Lorentzian Path Integral

Abstract

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