Vacuum decay in the Lorentzian path integral

TL;DR

This paper applies the Lorentzian path integral with Picard-Lefschetz theory to estimate false vacuum decay rates, extending beyond the critical bubble size where Euclidean methods fail.

Contribution

It introduces a Lorentzian path integral approach to vacuum decay, providing a new method that works for non-critical bubble sizes.

Findings

Nucleation rate matches Euclidean exponent for critical bubbles.

Extended computation to non-critical bubble sizes.

Demonstrated convergence of Lorentzian path integral via Picard-Lefschetz theory.

Abstract

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 integral 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.