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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.11463 |
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| _version_ | 1866913145070551040 |
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| author | Wachowski, Władysław |
| author_facet | Wachowski, Władysław |
| contents | We suggest a new generalization of the $\mathrm{U}(n)$ Yang-Mills theory obtained by relaxing the condition of covariant constancy of the Hermitian form in the fibers, $\nabla_a g_{αβ'} \ne 0$. This theory is a simpler analogue of the metric-affine gravity with $\nabla_a g_{bc} \ne 0$. In our case, connection $\nabla_a$ and Hermitian form $g_{αβ'}$ are two independent variables so total curvature and total potential are no longer anti-Hermitian matrices: thus, along with the standard YM potential $\boldsymbol{A}_a$ and field strength tensor $\boldsymbol{F}_{ab}$, it contains non-trivially interacting fields $\boldsymbol{B}_a$, $\boldsymbol{h}$, and $\boldsymbol{G}_{ab}$, $\boldsymbol{N}_a$, forming a non-Abelian generalization of Stückelberg theory. Due to the spontaneous symmetry breaking $\mathrm{GL}(n,\mathbb{C}) \to \mathrm{U}(n)$, these new fields can be made massive, and the limit $M\to\infty$ restores the standard YM theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New "metric-affine-like" generalization of Yang-Mills theory Wachowski, Władysław High Energy Physics - Theory We suggest a new generalization of the $\mathrm{U}(n)$ Yang-Mills theory obtained by relaxing the condition of covariant constancy of the Hermitian form in the fibers, $\nabla_a g_{αβ'} \ne 0$. This theory is a simpler analogue of the metric-affine gravity with $\nabla_a g_{bc} \ne 0$. In our case, connection $\nabla_a$ and Hermitian form $g_{αβ'}$ are two independent variables so total curvature and total potential are no longer anti-Hermitian matrices: thus, along with the standard YM potential $\boldsymbol{A}_a$ and field strength tensor $\boldsymbol{F}_{ab}$, it contains non-trivially interacting fields $\boldsymbol{B}_a$, $\boldsymbol{h}$, and $\boldsymbol{G}_{ab}$, $\boldsymbol{N}_a$, forming a non-Abelian generalization of Stückelberg theory. Due to the spontaneous symmetry breaking $\mathrm{GL}(n,\mathbb{C}) \to \mathrm{U}(n)$, these new fields can be made massive, and the limit $M\to\infty$ restores the standard YM theory. |
| title | New "metric-affine-like" generalization of Yang-Mills theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.11463 |