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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2406.07636 |
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| _version_ | 1866912153904087040 |
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| author | Wandler, F David |
| author_facet | Wandler, F David |
| contents | We use a numerical cooling algorithm to study fractional instantons in $SU(2)$ pure Yang-Mills on $\mathbb{R}^2\times\mathbb{T}^2_*$, $\mathbb{R}^3\times S^1$, and $\mathbb{R}\times \mathbb{T}^2_* \times S^1$. We confirm that the fractional instantons are center vortices on $\mathbb{R}^2\times\mathbb{T}^2_*$ and monopoles on $\mathbb{R}^3\times S^1$, and we calculate several properties relevant to using these solutions for semiclassical calculations. On $\mathbb{R}\times \mathbb{T}^2_* \times S^1$, we interpolate between the large $\mathbb{T}^2_*$ limit and the large $S^1$ limit to study how the solutions interpolate between center vortices and monopoles. We find that they are separated by a sharp transition, with 't Hooft's constant field strength solutions living at the transition point. These results contrast but do not contradict recent results suggesting continuity between vortices and monopoles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical fractional instantons in SU(2): center vortices, monopoles, and a sharp transition between them Wandler, F David High Energy Physics - Lattice High Energy Physics - Theory We use a numerical cooling algorithm to study fractional instantons in $SU(2)$ pure Yang-Mills on $\mathbb{R}^2\times\mathbb{T}^2_*$, $\mathbb{R}^3\times S^1$, and $\mathbb{R}\times \mathbb{T}^2_* \times S^1$. We confirm that the fractional instantons are center vortices on $\mathbb{R}^2\times\mathbb{T}^2_*$ and monopoles on $\mathbb{R}^3\times S^1$, and we calculate several properties relevant to using these solutions for semiclassical calculations. On $\mathbb{R}\times \mathbb{T}^2_* \times S^1$, we interpolate between the large $\mathbb{T}^2_*$ limit and the large $S^1$ limit to study how the solutions interpolate between center vortices and monopoles. We find that they are separated by a sharp transition, with 't Hooft's constant field strength solutions living at the transition point. These results contrast but do not contradict recent results suggesting continuity between vortices and monopoles. |
| title | Numerical fractional instantons in SU(2): center vortices, monopoles, and a sharp transition between them |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.07636 |