Vacuum decay actions from tunneling potentials for general spacetime dimension

Abstract

The tunneling potential method to calculate the action for vacuum decay is an alternative to the Euclidean bounce method that has a number of attractive features. In this paper we extend the formalism to general spacetime dimension d > 2 and use it to give simple proofs of several results. For Minkowski or Anti de Sitter false vacua, we show that gravity or higher barriers increase vacuum lifetime and describe a very clean picture of gravitational quenching of vacuum decay. We also derive the thin-wall limit of the action, show how detailed balance for dS to dS transitions works in the new formalism and how to obtain potentials for which the vacuum decay solution can be obtained analytically.

Bubbles of nothing: the tunneling potential approach

“…The agreement between the action S[V t ] of the V t formalism and the Euclidean action difference ∆S E of Coleman-De Luccia for regular CdL transitions was proven in [34] (for the proof in general dimension, see [45]). In this section we extend this proof to BoN decays.…”

“…In this section we summarize the main features of the tunneling potential formalism, proposed in [33,34], to describe semiclassical false vacuum decay including the effects of gravitation. For simplicity we restrict ourselves to 4d single field theories, and refer the reader to [36,45] for the generalisations to an arbitrary number of dimensions, d ≥ 3, and fields.…”

“…Let us first review briefly the proof for regular CdL solutions. In [34,45] the Euclidean action is rewritten in the form…”