The Unreasonable Effectiveness of the Tunneling Potential

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.