Complex Langevin kernels for real-time SU(N) lattice gauge theory in 3+1 dimensions
Abstract
We investigate complex Langevin (CL) dynamics for real-time SU(N) gauge theories in 3+1 dimensions and introduce new kernel modifications tailored for lattice gauge theory (LGT). Using the anisotropic kernel as a baseline, we demonstrate that on a rectangular regularized Schwinger-Keldysh time contour, stable simulations are possible for pure SU(2) gauge theory up to a real-time extent of 2β at a bare coupling g=0.5, where β denotes the inverse temperature. We show that a contour-dependent phase kernel extends this reach to 3β, while a local, field-dependent kernel based on traced plaquettes achieves 3.5β. These constructions represent the first application of such kernels to LGTs, especially in 3+1 dimensions. To validate the approach, we generalize the CL correctness criterion based on the drift magnitude to kernelled dynamics, providing a practical tool to assess correct convergence. Our results substantially advance the applicability of CL to real-time simulations in Minkowski space, establishing a framework for controlled studies of non-Abelian gauge theories at unprecedented time scales. A forthcoming paper applies these developments to the computation of unequal-time correlation functions.
Related
- Ab initio complex Langevin computation of the roton gap for a dipolar Bose condensate
- Hot and dense QCD equation of state from the complex Langevin equation
- Equation of state of hot and dense QCD using the complex Langevin equation
- Improving the accuracy of the Lorentz Integral Transform method using complex kernels
- Langevin Theory of Non-Markovian Quantum Dynamics: Application to Delayed Coherent Feedback and the Laser Linewidth
BibTeX
@misc{boguslavski2026complex,
title = {{Complex Langevin kernels for real-time SU(N) lattice gauge theory in 3+1 dimensions}},
author = {Kirill Boguslavski and Paul Hotzy and David I. Müller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37800},
eprint = {2610.37800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37800},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex Langevin kernels for real-time SU(N) lattice gauge theory in 3+1 dimensions
AU - Kirill Boguslavski
AU - Paul Hotzy
AU - David I. Müller
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37800
UR - https://arxiv.org/abs/2610.37800
AB - We investigate complex Langevin (CL) dynamics for real-time SU(N) gauge theories in 3+1 dimensions and introduce new kernel modifications tailored for lattice gauge theory (LGT). Using the anisotropic kernel as a baseline, we demonstrate that on a rectangular regularized Schwinger-Keldysh time contour, stable simulations are possible for pure SU(2) gauge theory up to a real-time extent of 2β at a bare coupling g=0.5, where β denotes the inverse temperature. We show that a contour-dependent phase kernel extends this reach to 3β, while a local, field-dependent kernel based on traced plaquettes achieves 3.5β. These constructions represent the first application of such kernels to LGTs, especially in 3+1 dimensions. To validate the approach, we generalize the CL correctness criterion based on the drift magnitude to kernelled dynamics, providing a practical tool to assess correct convergence. Our results substantially advance the applicability of CL to real-time simulations in Minkowski space, establishing a framework for controlled studies of non-Abelian gauge theories at unprecedented time scales. A forthcoming paper applies these developments to the computation of unequal-time correlation functions.
ER -