# Complex Langevin dynamics and zeroes of the fermion determinant

## TL;DR

This paper investigates how zeroes of the fermion determinant affect the validity of complex Langevin dynamics in QCD, showing that with careful monitoring, the method remains justifiable despite meromorphic drift issues.

## Contribution

It analyzes the impact of determinant zeroes on complex Langevin dynamics and demonstrates that the approach can be justified with proper oversight in QCD.

## Key findings

- Poles in the drift influence the formal justification of complex Langevin.
- Lessons from simple models inform the application to QCD.
- The method remains justifiable with careful monitoring despite meromorphicity.

## Abstract

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.