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A stabilizing kernel for complex Langevin simulations of real-time gauge theories
High Energy Physics - Lattice · Submitted 14 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that may allow us to calculate real-time observables from first principles.
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The abstract, sentence by sentence
The complex Langevin (CL) method is a promising approach to overcome the sign problem, which emerges in real-time formulations of quantum field theories. Over the past decade, stabilization techniques for CL have been developed with important applications in finite density QCD. However, they are insufficient for SU($N_c$) gauge theories on a Schwinger-Keldysh time contour that is required for a real-time formulation. In these proceedings we revise the discretization of the real-time CL equations and introduce a novel anisotropic kernel that enables CL simulations on discretized time contours. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that may allow us to calculate real-time observables from first principles.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The complex Langevin (CL) method is a promising approach to overcome the sign problem, which emerges in real-time formulations of quantum field theories. | background 1.00 | 0.05 | 0.03 | asserted 0.70 |
| s1 | Over the past decade, stabilization techniques for CL have been developed with important applications in finite density QCD. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s2 | However, they are insufficient for SU($N_c$) gauge theories on a Schwinger-Keldysh time contour that is required for a real-time formulation. | gap 0.97 | 0.11 | 0.05 | asserted 1.00 |
| s3 | In these proceedings we revise the discretization of the real-time CL equations and introduce a novel anisotropic kernel that enables CL simulations on discretized time contours. | contribution 0.96 | 0.95 | 0.18 | asserted 1.00 |
| s4 | Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that may allow us to calculate real-time observables from first principles. | result 0.94 | 0.96 | 0.82 | hedged possibility 0.70 |
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The paper
Original abstract
The complex Langevin (CL) method is a promising approach to overcome the sign problem, which emerges in real-time formulations of quantum field theories. Over the past decade, stabilization techniques for CL have been developed with important applications in finite density QCD. However, they are insufficient for SU($N_c$) gauge theories on a Schwinger-Keldysh time contour that is required for a real-time formulation. In these proceedings we revise the discretization of the real-time CL equations and introduce a novel anisotropic kernel that enables CL simulations on discretized time contours. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that may allow us to calculate real-time observables from first principles.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 11 sentences without a confident label
Uses the method or tool of 5 papers
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Gauge cooling (GC) We further adopt the gauge cooling procedure introduced in [ref] and developed further in [ref] to alleviate instabilities of our CL simulations.
Controlling complex Langevin dynamics at finite density · Stabilization techniques · 1.00
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Gauge cooling (GC) We further adopt the gauge cooling procedure introduced in [ref] and developed further in [ref] to alleviate instabilities of our CL simulations.
Gauge cooling in complex Langevin for QCD with heavy quarks · Stabilization techniques · 1.00
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Following [ref] we discretize the gauge field by introducing link and plaquette variables [equation] on an $N_t ×N_s^3$ lattice and use the Wilson action [equation] where the coupling constants are denoted by $β_0=β_0i=β_i0=2N_c/g^2a_i/a_0$ and $β_s=β_ij=β_ji=2N_c/g^2a_0/a_i$ and we assume spatial lattice spacings $a_i=a_s$ for $i=1,2,3$.
Lattice simulations of real-time quantum fields · CL simulations on the lattice · 0.99
Compares with 1 paper
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We discuss the improvements using the example of the real trace of the average spatial plaquette [equation] We first reproduce results of [ref] as dotted curves in [ref] for different tilt angles $α$ on the isosceles time contour.
Lattice simulations of real-time quantum fields · Improved stability and convergence of our kerneled CL equation · 0.94
Cites as background 7 papers
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Such a situation occurs for real-time simulations of quantum field theories, where the CL method has been used [ref] .
Real-time gauge theory simulations from stochastic quantization with optimized updating · Introduction · 0.81
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Such a situation occurs for real-time simulations of quantum field theories, where the CL method has been used [ref] .
Stable solvers for real-time Complex Langevin · Introduction · 0.81
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Such a situation occurs for real-time simulations of quantum field theories, where the CL method has been used [ref] .
Towards sampling complex actions · Introduction · 0.81
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