Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane

TL;DR

This paper compares Lefschetz thimble and stochastic quantisation methods for complex actions in lattice field theories, analyzing their sampling distributions and the impact of residual phases in a simple model.

Contribution

It provides a comparative analysis of Lefschetz thimbles and stochastic quantisation for complex actions, highlighting their differences and the role of residual phases.

Findings

Lefschetz thimbles and stochastic quantisation produce different sampling distributions.

The residual phase on the Lefschetz thimble affects the sampling process.

Comparison conducted on a simple model to illustrate the differences.

Abstract

Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from stochastic quantisation (or complex Langevin dynamics) in the case of a simple model and contrast the distributions being sampled. We also study the role of the residual phase on the Lefschetz thimble.