Vacuum decay in the Lorentzian path integral

We apply the Lorentzian path integral to the decay of a false vacuum and estimate the false-vacuum decay rate. To make the Lorentzian path integral convergent, the deformation of an integration contour is performed by following the Picard-Lefschetz theory. We show that the nucleation rate of a critical bubble, for which the corresponding bounce action is extremized, has the same exponent as the Euclidean approach. We also extend our computation to the nucleation of a bubble larger or smaller than the critical one to which the Euclidean formalism is not applicable.

Automated summary

We apply the Lorentzian path integral to analyze the decay of a false vacuum and predict the decay rate. By utilizing the Picard-Lefschetz theory, we deform the integration contour to ensure the convergence of the Lorentzian path integral. Our findings indicate that the nucleation rate of a critical bubble, where the corresponding bounce action is extremized, follows the same exponent as the Euclidean approach. Furthermore, we extend our computation to the nucleation of bubbles larger or smaller than the critical one, where the Euclidean formalism is not applicable.