Complex Langevin dynamics for SU(3) gauge theory in the presence of a theta term

TL;DR

This paper explores the use of complex Langevin dynamics to study SU(3) gauge theory with a theta term, addressing the sign problem in lattice QCD simulations and providing insights into the strong CP problem.

Contribution

It demonstrates the application of complex Langevin methods to SU(3) gauge theory with a theta term and reports on the effectiveness of gradient flow techniques in this context.

Findings

Complex Langevin dynamics can handle the sign problem for non-zero theta.

Results include both real and imaginary theta values.

Gradient flow aids in analyzing topological properties.

Abstract

One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta term. On the lattice such a term is complex: hence it introduces a sign problem which, in general, limits the applicability of standard Monte Carlo methods. Here we will discuss the approach of complex Langevin dynamics and show results for both real and imaginary values of theta. We also report on our experience with the gradient flow for real and imaginary theta.