Analytic thin wall false vacuum decay rate

TL;DR

This paper derives a precise, one-loop decay rate for false vacuum transitions in the thin wall limit, including detailed calculations of fluctuations, renormalization, and explicit formulas in various dimensions.

Contribution

It provides a closed-form, one-loop decay rate in the thin wall limit with comprehensive treatment of fluctuations, renormalization, and explicit dimensional formulas.

Findings

Explicit decay rate formulas in 3 and 4 dimensions

Functional determinant expressions for generic multipoles

Renormalized decay rate with higher order corrections

Abstract

We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in $D$ dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel'fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in $D = 3, 4$ and give a closed-form expression for the finite functional determinant in any dimension.