Variational cohomology and topological solitons in Yang-Mills-Chern-Simons theories
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915290021888000 |
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| author | Winterroth, Ekkehart |
| author_facet | Winterroth, Ekkehart |
| contents | In cohomological formulations of the calculus of variations obstructions to the existence of (global) solutions of the Euler-Lagrange equations can arise in principle. It seems, however, quite common to assume that such obstructions always vanish, at least in the cases of interest in theoretical physics. This is not so: for Yang-Mills-Chern-Simons theories on compact manifolds in odd dimensions $\geq 5$ we find a non trivial obstruction which leads to a quite strong non existence theorem for topological solitons/instantons. The consequences of this result for the Yang-Mills-Chern-Simons theories of holographic QCD (on $I\!\!R^{5}$) are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_03037 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Variational cohomology and topological solitons in Yang-Mills-Chern-Simons theories Winterroth, Ekkehart High Energy Physics - Theory Mathematical Physics Differential Geometry 53C07, 53Z05, 57R20, 81T13, 81T20 In cohomological formulations of the calculus of variations obstructions to the existence of (global) solutions of the Euler-Lagrange equations can arise in principle. It seems, however, quite common to assume that such obstructions always vanish, at least in the cases of interest in theoretical physics. This is not so: for Yang-Mills-Chern-Simons theories on compact manifolds in odd dimensions $\geq 5$ we find a non trivial obstruction which leads to a quite strong non existence theorem for topological solitons/instantons. The consequences of this result for the Yang-Mills-Chern-Simons theories of holographic QCD (on $I\!\!R^{5}$) are discussed. |
| title | Variational cohomology and topological solitons in Yang-Mills-Chern-Simons theories |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry 53C07, 53Z05, 57R20, 81T13, 81T20 |
| url | https://arxiv.org/abs/2103.03037 |