Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

Understand

Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about non-perturbative saddle point field configurations of path integrals can be extracted from perturbation theory.

• Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them.
• However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected.
• Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations.