Lorentzian Path Integrals and Jackiw-Teitelboim wormholes with imaginary scalars

The Lorentzian path integral was recently used to argue that standard Euclidean axion wormholes do not dominate computations of connected AdS/CFT partition functions. We now apply similar methods to study the seemingly-analogous Jackiw-Teitelboim wormholes constructed by Garcia-Garcia and Godet using Jackiw-Teitelboim gravity with an imaginary-valued minimally-coupled massless scalar field. However, this time we find that these wormholes do dominate our path integral for the relevant connected partition function. This supports the suggestion by Garcia-Garcia and Godet that contributions from such wormholes parallel the physics of the Sachdev-Ye-Kitaev model at complex couplings. The result also illustrates the sensitivity of wormhole contributions to details of the relevant physics.