Expanded regimes of area law for lattice Yang-Mills theories
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| Format: | Preprint |
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2025
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| _version_ | 1866911178902470656 |
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| author | Cao, Sky Nissim, Ron Sheffield, Scott |
| author_facet | Cao, Sky Nissim, Ron Sheffield, Scott |
| contents | We extend the parameter regimes for which area law is proven for pure $\mathrm{U}(N)$ lattice Yang-Mills theories, in particular when $N$ is large. This improves on a classical result of Osterwalder-Seiler from 1978. To do so, we view the master loop equation as a linear inhomogeneous equation for Wilson string expectations, and then prove an a priori bound for solutions to the equation. The main novelty is in how we deal with the merger term in the master loop equation. This is done by introducing a truncated model for which the merger term is unproblematic, and then showing that the truncated model well approximates the original model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expanded regimes of area law for lattice Yang-Mills theories Cao, Sky Nissim, Ron Sheffield, Scott Probability Mathematical Physics 81T13, 82B20 We extend the parameter regimes for which area law is proven for pure $\mathrm{U}(N)$ lattice Yang-Mills theories, in particular when $N$ is large. This improves on a classical result of Osterwalder-Seiler from 1978. To do so, we view the master loop equation as a linear inhomogeneous equation for Wilson string expectations, and then prove an a priori bound for solutions to the equation. The main novelty is in how we deal with the merger term in the master loop equation. This is done by introducing a truncated model for which the merger term is unproblematic, and then showing that the truncated model well approximates the original model. |
| title | Expanded regimes of area law for lattice Yang-Mills theories |
| topic | Probability Mathematical Physics 81T13, 82B20 |
| url | https://arxiv.org/abs/2505.16585 |