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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2505.10396 |
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| _version_ | 1866912377680691200 |
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| author | Bergner, Georg González-Arroyo, Antonio Soler, Ivan |
| author_facet | Bergner, Georg González-Arroyo, Antonio Soler, Ivan |
| contents | We study the behaviour of \SU{2} Yang-Mills fields on a $T_2\times R^2$ geometry where the two-torus is equipped with twisted boundary conditions. We monitor the evolution of the dynamics of the system as a function of the torus size $l_s$. For small sizes the behaviour of the system is well understood in terms of semiclassical predictions. In our case, the long distance structure is that of a two-dimensional gas of vortex-like fractional instantons with size and density growing with $l_s$. Our lattice Monte Carlo simulations confirm the semiclassical predictions and allow the determination of the relevant scale signalling the transition to the non-dilute situation. At low densities the string tension takes the standard value of a 2D center-vortex gas, growing with the density and approaching the value measured at infinite volume. Our work includes preliminary studies of the extension to \SU{N} and to the region of large sizes in which boundary conditions are irrelevant, and all physical scales are determined by the $Λ$ parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $T_2 \times R^2$ roadmap to Confinement in SU(2) Yang-Mills theory Bergner, Georg González-Arroyo, Antonio Soler, Ivan High Energy Physics - Lattice High Energy Physics - Theory We study the behaviour of \SU{2} Yang-Mills fields on a $T_2\times R^2$ geometry where the two-torus is equipped with twisted boundary conditions. We monitor the evolution of the dynamics of the system as a function of the torus size $l_s$. For small sizes the behaviour of the system is well understood in terms of semiclassical predictions. In our case, the long distance structure is that of a two-dimensional gas of vortex-like fractional instantons with size and density growing with $l_s$. Our lattice Monte Carlo simulations confirm the semiclassical predictions and allow the determination of the relevant scale signalling the transition to the non-dilute situation. At low densities the string tension takes the standard value of a 2D center-vortex gas, growing with the density and approaching the value measured at infinite volume. Our work includes preliminary studies of the extension to \SU{N} and to the region of large sizes in which boundary conditions are irrelevant, and all physical scales are determined by the $Λ$ parameter. |
| title | A $T_2 \times R^2$ roadmap to Confinement in SU(2) Yang-Mills theory |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.10396 |