Analytic thin wall false vacuum decay rate

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.

Erratum to: Analytic thin wall false vacuum decay rate

“…line in eq. (6.14) in [1]. The second term was dropped in [1], however it also contains a contribution that scales as 1/∆ 3 , and must therefore be counted as leading order.…”

“…This corrects the second line of eq. (6.14) in [1]: the +1 is replaced by +5/4. In turn, this changes the last term of eq.…”

“…The additional term is present inside Ĩ2 , introduced in eq. (6.12) of [1], and contributes to the complete renormalized determinant. The Ĩ2 integral is defined in the first line of eq.…”

“…Here, I 2 is the UV integral given in eq. (6.13) of [1], where R = r/( √ λv) r 0 /( √ λv∆) is the bubble radius, with r 0 = 1 in D = 4. The first term in (2) corresponds to the second 1 https://orcid.org/0000-0002-6198-8118.…”

Vacuum decay actions from tunneling potentials for general spacetime dimension

“…Analytical potentials (or bounces) for general d have been obtained before, see e.g [25,26]. for examples (without gravity).…”