Gravitational Decoupling and Picard-Lefschetz

TL;DR

This paper examines tunneling processes in gravitational theories, highlighting limitations of the Euclidean method and proposing the Picard-Lefschetz approach as a remedy for accurate amplitude calculations.

Contribution

It demonstrates the failure of the Euclidean approach in decoupling limits and introduces the Picard-Lefschetz method as a systematic alternative for gravitational tunneling.

Findings

Euclidean method does not approach the field theory limit as $M_{p} ightarrow $

Picard-Lefschetz theory can correctly compute tunneling amplitudes in gravitational settings

Lorentzian prescriptions improve the decoupling behavior in gravitational tunneling calculations

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.