Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel

Abstract

The complex Langevin (CL) method is a promising approach to overcome the sign problem that occurs in real-time formulations of quantum field theories. Using the Schwinger-Keldysh formalism, we study SU($N_c$) gauge theories with CL. We observe that current stabilization techniques are insufficient to obtain correct results. Therefore, we revise the discretization of the CL equations on complex time contours, find a time reflection symmetric formulation and introduce a novel anisotropic kernel that enables CL simulations on discretized complex time paths. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that we validate using additional observables and that can be systematically improved. For the first time, we are able to simulate non-Abelian gauge theory on time contours whose real-time extent exceeds its inverse temperature. Thus, our approach may pave the way towards an ab-initio real-time framework of QCD in and out of equilibrium with a potentially large impact on the phenomenology of heavy-ion collisions.

arXiv comment28 pages + references and appendices, 7 figures, 1 table; v2: revised, data and plot files attached, published version

References in corpus (44)

• Hydrodynamic Modeling of Heavy-Ion Collisions
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• Bottom-up thermalization in heavy ion collisions
• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• Effective Kinetic Theory for High Temperature Gauge Theories
• Holography and colliding gravitational shock waves in asymptotically AdS_5 spacetime
• Event-by-event gluon multiplicity, energy density and eccentricities at RHIC and LHC
• Jet quenching in high-energy heavy-ion collisions
• The Complex Langevin method: When can it be trusted?
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Simulating full QCD at nonzero density using the complex Langevin equation
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• A novel Bayesian approach to spectral function reconstruction
• Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
• Lattice simulations of real-time quantum fields
• From full stopping to transparency in a holographic model of heavy ion collisions
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Approaches to the sign problem in lattice field theory
• Controlling complex Langevin dynamics at finite density
• The argument for justification of the complex Langevin method and the condition for correct convergence
• Adaptive stepsize and instabilities in complex Langevin dynamics
• Simulating nonequilibrium quantum fields with stochastic quantization techniques
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Bottomonium suppression in an open quantum system using the quantum trajectories method
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• Complex Langevin dynamics and zeroes of the fermion determinant
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Stability of complex Langevin dynamics in effective models
• Complex Langevin and boundary terms
• Complex Langevin Equations and Schwinger-Dyson Equations
• Status of Complex Langevin
• Justification of the complex Langevin method with the gauge cooling procedure
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Dynamical stabilisation of complex Langevin simulations of QCD
• Deconfinement transition line with the Complex Langevin equation up to $\mu /T\sim 5$
• Highly occupied gauge theories in 2+1 dimensions: self-similar attractor
• Testing the criterion for correct convergence in the complex Langevin method
• Towards learning optimized kernels for complex Langevin
• Progress on 3+1D Glasma simulations
• Stable solvers for real-time Complex Langevin
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• Restricted phase-space approximation in real-time stochastic quantization
• Complex Langevin approach to interacting Bose gases
• Getting even with CLE

Cited by in corpus (6)

• Towards learning optimized kernels for complex Langevin
• Real-time correlators in 3+1D thermal lattice gauge theory
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin
• Correctness criteria for complex Langevin
• Combining complex Langevin dynamics with score-based and energy-based diffusion models