Abstract
In this work, we consider tunneling between non-metastable states in gravitational theories. Such processes arise in various contexts, e.g., in inflationary scenarios where the inflaton potential involves multiple fields or multiple branches. They are also relevant for bubble wall nucleation in some cosmological settings. However, we show that the transition amplitudes computed using the Euclidean method generally do not approach the corresponding field theory limit as $M_{p}\rightarrow \infty$. This implies that in the Euclidean framework, there is no systematic expansion in powers of $G_{N}$ for such processes. Such considerations also carry over directly to no-boundary scenarios involving Hawking-Turok instantons. In this note, we illustrate this failure of decoupling in the Euclidean approach with a simple model of axion monodromy and then argue that the situation can be remedied with a Lorentzian prescription such as the Picard-Lefschetz theory. As a proof of concept, we illustrate with a simple model how tunneling transition amplitudes can be calculated using the Picard-Lefschetz approach.
Highlights
Euclideanization is a technique that is ubiquitous throughout physics
We argue that the Lorentzian path integral does not suffer from a failure to decouple, which is very much in the spirit of [21] where Lorentzian methods were advocated for slightly different reasons
That in the two-field example related to axion monodromy, decoupling fails
Summary
Euclideanization is a technique that is ubiquitous throughout physics. It is used to understand problems including the origin of the Universe, numerical computations in field theory, nonperturbative transitions and instantons, perturbative evaluation of the path integral, etc. This is a highly undesirable situation, as the real world contains gravity, and we would like to consider decoupled field-theoretic systems at low energy without resorting to a full-fledged theory of quantum gravity This suggests that the Euclidean result is not even a first approximation in some more systematic approach—it is instead just the wrong starting point for this kind of problem. While these authors are studying classically smooth geometries and their focus is on the suppression of angular fluctuations, we are discussing singular (yet generic) geometries where the problem is a lack of a decoupling limit, even for spherically symmetric perturbations In these examples we are forced to consider alternative methods for computing the tunneling amplitude.
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