Finiteness of the Yang-Mills-Chern-Simons action in linear covariant gauges by taking into account gauge copies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910815252119552 |
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| author | Azevedo, Daniel O. R. Pereira, Antonio D. |
| author_facet | Azevedo, Daniel O. R. Pereira, Antonio D. |
| contents | In recent years, the effects of removing infinitesimal Gribov copies from the path integral of gauge-fixed Yang-Mills-Chern-Simons theories formulated in three-dimensional Euclidean space have been investigated. Part of the interest resides on the fact that such an elimination of gauge copies introduces a mass parameter, the Gribov parameter, which is relevant when the assumptions of the Faddeev-Popov procedure are not well-grounded. Such a parameter enters the propagator of the gauge field which is topologically massive due to the Chern-Simons term. The resulting action, which eliminates infinitesimal Gribov copies in this context, has been constructed in linear covariant gauges and the interplay between the aforementioned mass-parameters allows for a rich phase diagram in which confining and deconfining signatures are observed in the gauge-field propagator. In the present work, we establish the renormalization properties of such a theory at all orders in perturbation theory by means of the algebraic renormalization framework and show that the removal of infinitesimal Gribov copies does not affect the standard non-renormalization properties of standard gauge-fixed Yang-Mills-Chern-Simons theories, i.e., the theory is finite. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness of the Yang-Mills-Chern-Simons action in linear covariant gauges by taking into account gauge copies Azevedo, Daniel O. R. Pereira, Antonio D. High Energy Physics - Theory High Energy Physics - Phenomenology In recent years, the effects of removing infinitesimal Gribov copies from the path integral of gauge-fixed Yang-Mills-Chern-Simons theories formulated in three-dimensional Euclidean space have been investigated. Part of the interest resides on the fact that such an elimination of gauge copies introduces a mass parameter, the Gribov parameter, which is relevant when the assumptions of the Faddeev-Popov procedure are not well-grounded. Such a parameter enters the propagator of the gauge field which is topologically massive due to the Chern-Simons term. The resulting action, which eliminates infinitesimal Gribov copies in this context, has been constructed in linear covariant gauges and the interplay between the aforementioned mass-parameters allows for a rich phase diagram in which confining and deconfining signatures are observed in the gauge-field propagator. In the present work, we establish the renormalization properties of such a theory at all orders in perturbation theory by means of the algebraic renormalization framework and show that the removal of infinitesimal Gribov copies does not affect the standard non-renormalization properties of standard gauge-fixed Yang-Mills-Chern-Simons theories, i.e., the theory is finite. |
| title | Finiteness of the Yang-Mills-Chern-Simons action in linear covariant gauges by taking into account gauge copies |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2502.03284 |