This paper presents a simple framework that organizes thin-wall Coleman-De Luccia instantons based on the Euclidean geometries of their original and tunneled vacuum patches. We consider all a priori allowed vacuum pairs (de Sitter or Anti-de Sitter for either patch, Minkowski can be obtained as a limit of either), and $O(4)$-symmetric thin-wall geometries connecting them. For each candidate bounce geometry, either a condition under which a solution to the $O(4)$-invariant equations of motion exists is derived, or the would-be vacuum transition is ruled out. For the parameter regimes in which a solution exists, we determine whether expansion/contraction of the bounce supplies a negative mode in the second variation of the Euclidean action. All results follow from the monotonicity of a single function.

中文翻译：

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Coleman-De Luccia 转换的统一系统

本文提出了一个简单的框架，该框架基于其原始和隧道真空贴片的欧几里德几何结构来组织薄壁 Coleman-De Luccia 瞬子。我们考虑所有先验允许的真空对（任一贴片的 de Sitter 或 Anti-de Sitter，Minkowski 都可以作为两者的限制获得），以及连接它们的 $O(4)$-对称薄壁几何形状。对于每个候选弹跳几何，要么推导出 $O(4)$-不变运动方程的解存在的条件，要么排除可能的真空转变。对于存在解的参数机制，我们确定反弹的膨胀/收缩是否在欧几里得作用的第二个变体中提供负模式。所有结果都来自单个函数的单调性。