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 insuff...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2023)011 |
| _version_ | 1797675779948019712 |
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| author | Kirill Boguslavski Paul Hotzy David I. Müller |
| author_facet | Kirill Boguslavski Paul Hotzy David I. Müller |
| author_sort | Kirill Boguslavski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T22:18:33Z |
| format | Article |
| id | doaj.art-1b4eb2da4dc44e9a8b078733553a8cc2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T22:18:33Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1b4eb2da4dc44e9a8b078733553a8cc22023-09-24T11:07:34ZengSpringerOpenJournal of High Energy Physics1029-84792023-06-012023614210.1007/JHEP06(2023)011Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernelKirill Boguslavski0Paul Hotzy1David I. Müller2Institute for Theoretical Physics, TU WienInstitute for Theoretical Physics, TU WienInstitute for Theoretical Physics, TU WienAbstract 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.https://doi.org/10.1007/JHEP06(2023)011Algorithms and Theoretical DevelopmentsLattice QCDNon-Zero Temperature and DensityNon-Equilibrium Field Theory |
| spellingShingle | Kirill Boguslavski Paul Hotzy David I. Müller Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel Journal of High Energy Physics Algorithms and Theoretical Developments Lattice QCD Non-Zero Temperature and Density Non-Equilibrium Field Theory |
| title | Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel |
| title_full | Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel |
| title_fullStr | Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel |
| title_full_unstemmed | Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel |
| title_short | Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel |
| title_sort | stabilizing complex langevin for real time gauge theories with an anisotropic kernel |
| topic | Algorithms and Theoretical Developments Lattice QCD Non-Zero Temperature and Density Non-Equilibrium Field Theory |
| url | https://doi.org/10.1007/JHEP06(2023)011 |
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