Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term
Abstract Monte Carlo simulation of gauge theories with a θ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2020)023 |
| _version_ | 1811340654304821248 |
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| author | Mitsuaki Hirasawa Akira Matsumoto Jun Nishimura Atis Yosprakob |
| author_facet | Mitsuaki Hirasawa Akira Matsumoto Jun Nishimura Atis Yosprakob |
| author_sort | Mitsuaki Hirasawa |
| collection | DOAJ |
| description | Abstract Monte Carlo simulation of gauge theories with a θ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a θ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the θ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for |θ| < π. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large θ, where the link variables near the puncture become very far from being unitary. |
| first_indexed | 2024-04-13T18:45:11Z |
| format | Article |
| id | doaj.art-4de7ad7cc88643efb6aa77ec2f066272 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T18:45:11Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4de7ad7cc88643efb6aa77ec2f0662722022-12-22T02:34:36ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020914110.1007/JHEP09(2020)023Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ termMitsuaki Hirasawa0Akira Matsumoto1Jun Nishimura2Atis Yosprakob3Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI)Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI)Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI)Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI)Abstract Monte Carlo simulation of gauge theories with a θ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a θ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the θ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for |θ| < π. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large θ, where the link variables near the puncture become very far from being unitary.http://link.springer.com/article/10.1007/JHEP09(2020)023Lattice Quantum Field TheoryField Theories in Lower Dimensions |
| spellingShingle | Mitsuaki Hirasawa Akira Matsumoto Jun Nishimura Atis Yosprakob Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term Journal of High Energy Physics Lattice Quantum Field Theory Field Theories in Lower Dimensions |
| title | Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term |
| title_full | Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term |
| title_fullStr | Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term |
| title_full_unstemmed | Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term |
| title_short | Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term |
| title_sort | complex langevin analysis of 2d u 1 gauge theory on a torus with a θ term |
| topic | Lattice Quantum Field Theory Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP09(2020)023 |
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