The Fate of Nearly Supersymmetric Vacua

TL;DR

This paper investigates the longevity of nearly supersymmetric vacua, revealing that their decay rates are generally slow, with specific decay amplitudes derived for flat space theories transitioning to deep AdS vacua.

Contribution

It provides a detailed analysis of decay amplitudes for nearly supersymmetric vacua, including explicit formulas under certain approximations, and discusses the impact of supersymmetry breaking on decay rates.

Findings

Decay amplitude for flat space to AdS vacua: ${ m A} = ext{constant} imes e^{-2 extpi^2/({ m Re} m_{3/2})^2}$

Decay rates are slow across various cases of nearly supersymmetric vacua

Metastable supersymmetry breaking generally leads to faster decay rates.

Abstract

Supersymmetric vacua are stable. It is interesting to ask: how long-lived are vacua which are nearly supersymmetric? This question is relevant if our universe is approximately supersymmetric. It is also of importance for a number of issues of the physics of the landscape and eternal inflation. In this note, we distinguish a variety of cases. In all of them the decay is slow. For a flat space theory decaying to a deep AdS vacuum, the leading behavior of the decay amplitude, if a thin wall approximation is valid, is ${\cal A} = \gamma e^{-2 \pi^2/({\rm Re} m_{3/2})^2}$ (where the phase of $m_{3/2}$ is defined in the text) for ${\rm Re} m_{3/2}>0$, and zero otherwise. Metastable supersymmetry breaking generally yields parametrically more rapid decays. For nearly supersymmetric decays, we will see that it is necessary to compute subleading terms in the exponential to extraordinarily high accuracy before one can meaningfully discuss the prefactor.