  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.
