Gravitational Decoupling and Picard-Lefschetz

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 $M_p\to \infty$. 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.

26 pages, 5 figures

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• A Primer on Resurgent Transseries and Their Asymptotics
• Functional methods for false vacuum decay in real time
• Complex Saddles and Euclidean Wormholes in the Lorentzian Path Integral
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Phases of Inflation
• Parametrized Path Approach to Vacuum Decay
• Topological Data Analysis for the String Landscape
• Gravitational thermodynamics without the conformal factor problem: Partition functions and Euclidean saddles from Lorentzian Path Integrals
• Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole