Bootstrap for Finite N Lattice Yang-Mills Theory
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909415837270016 |
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| author | Kazakov, Vladimir Zheng, Zechuan |
| author_facet | Kazakov, Vladimir Zheng, Zechuan |
| contents | We introduce a comprehensive framework for analyzing finite $N$ lattice Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear and closed exclusively on single-trace Wilson loops. This inherent linearity significantly enhances the efficiency of the bootstrap approach due to the convex nature of the problem, permitting the inclusion of Wilson loops up to length 24. The exact upper and lower margins for the free energy per plaquette, derived from our bootstrap method, demonstrate good agreement with Monte Carlo data, achieving precision within $0.1\%$ for the physically relevant range of couplings in both three and four dimensions. Additionally, our bootstrap data provides estimates of the string tension, in qualitative agreement with existing Monte Carlo computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bootstrap for Finite N Lattice Yang-Mills Theory Kazakov, Vladimir Zheng, Zechuan High Energy Physics - Theory High Energy Physics - Lattice We introduce a comprehensive framework for analyzing finite $N$ lattice Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear and closed exclusively on single-trace Wilson loops. This inherent linearity significantly enhances the efficiency of the bootstrap approach due to the convex nature of the problem, permitting the inclusion of Wilson loops up to length 24. The exact upper and lower margins for the free energy per plaquette, derived from our bootstrap method, demonstrate good agreement with Monte Carlo data, achieving precision within $0.1\%$ for the physically relevant range of couplings in both three and four dimensions. Additionally, our bootstrap data provides estimates of the string tension, in qualitative agreement with existing Monte Carlo computations. |
| title | Bootstrap for Finite N Lattice Yang-Mills Theory |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2404.16925 |