Analytic false-vacuum decay rate in the thin-wall approximation

Abstract

We present a fully analytical calculation of the false vacuum decay rate for a self-interacting scalar field in the thin-wall approximation. We obtain the bounce solution, together with the Euclidean action, counter-terms and renormalization group running, and we extract the functional determinant via the Gel'fand-Yaglom theorem. Our procedure is valid for a generic spacetime dimension $D$, and we provide an explicit finite renormalized decay rate in $D=3,4$.

Comments: Conference proceedings for Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity", August 28 - October 1, 2022, Corfu, Greece. Based on arXiv:2202.04498