Bootstrapping the Abelian lattice gauge theories
Abstract We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ L max to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether...
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| Format: | Article |
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SpringerOpen
2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)154 |
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| author | Zhijin Li Shutong Zhou |
| author_facet | Zhijin Li Shutong Zhou |
| author_sort | Zhijin Li |
| collection | DOAJ |
| description | Abstract We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ L max to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large L max = 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10 −8 or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ2 and U(1) lattice gauge theories with L max = 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories. |
| format | Article |
| id | doaj-art-c3a1ef964a564163bbbcd6c131cc32e8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-c3a1ef964a564163bbbcd6c131cc32e82024-11-24T12:07:16ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024813210.1007/JHEP08(2024)154Bootstrapping the Abelian lattice gauge theoriesZhijin Li0Shutong Zhou1Shing-Tung Yau Center and School of Physics, Southeast UniversityDepartment of Physics, Nanjing UniversityAbstract We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ L max to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large L max = 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10 −8 or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ2 and U(1) lattice gauge theories with L max = 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories.https://doi.org/10.1007/JHEP08(2024)154Lattice Quantum Field TheoryWilson, ’t Hooft and Polyakov loopsConfinementNonperturbative Effects |
| spellingShingle | Zhijin Li Shutong Zhou Bootstrapping the Abelian lattice gauge theories Journal of High Energy Physics Lattice Quantum Field Theory Wilson, ’t Hooft and Polyakov loops Confinement Nonperturbative Effects |
| title | Bootstrapping the Abelian lattice gauge theories |
| title_full | Bootstrapping the Abelian lattice gauge theories |
| title_fullStr | Bootstrapping the Abelian lattice gauge theories |
| title_full_unstemmed | Bootstrapping the Abelian lattice gauge theories |
| title_short | Bootstrapping the Abelian lattice gauge theories |
| title_sort | bootstrapping the abelian lattice gauge theories |
| topic | Lattice Quantum Field Theory Wilson, ’t Hooft and Polyakov loops Confinement Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP08(2024)154 |
| work_keys_str_mv | AT zhijinli bootstrappingtheabelianlatticegaugetheories AT shutongzhou bootstrappingtheabelianlatticegaugetheories |