The Unreasonable Effectiveness of the Tunneling Potential

TL;DR

The paper discusses the tunneling potential formalism as an effective and versatile method for calculating vacuum decay, revealing its advantages over traditional Euclidean approaches in various decay scenarios.

Contribution

It demonstrates that the tunneling potential approach simplifies calculations, provides universal results, and naturally incorporates complex decay processes without boundary term adjustments.

Findings

The tunneling potential describes decay as a minimum of the action, not a saddle point.

Universal action $S[V_t]$ governs various vacuum decays, including Hawking-Moss instantons.

The approach correctly handles boundary conditions and complex decay processes like bubbles of nothing.

Abstract

The Tunneling Potential Formalism was introduced to calculate the tunneling actions that control vacuum decay as an alternative to the standard Euclidean Formalism. The new approach sets the problem as a simple variational problem in field space with decay described by a tunneling potential function $V_t$ that extremizes a simple action functional $S[V_t]$ and has a number of appealing properties that have been presented elsewhere. In this note I discuss several instances in which this $V_t$ approach seems to give more than one would have expected a priori, as the following: the $V_t$ describing the decay is a minimum of the new action $S[V_t]$ rather than a saddle point; the decay of AdS, dS or Minkowski vacua are governed by a unique universal $S[V_t]$ which also gives the Hawking-Moss instanton in the appropriate limit; physically relevant solutions beyond the Coleman-De Luccia (CdL) bounce, like pseudo-bounces or bubbles of nothing (BoNs), show up in a straightforward way as generalizations of the CdL bounce, with the correct boundary conditions; in cases for which the Euclidean action calculation requires the inclusion of particular boundary terms (like for BoNs or for the decay of AdS maxima above the Breitenlohner-Freedman bound) $S[V_t]$ gives the correct result without the need of including any boundary term.