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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.16504 |
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| _version_ | 1866918101814083584 |
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| author | Pinoy, Alan Vatani, Shahram |
| author_facet | Pinoy, Alan Vatani, Shahram |
| contents | We investigate the reliability of the large $N_f$ expansion of four-dimensional gauge-fermion quantum field theories, focusing on the structure and scheme dependence of the beta function. While the existence of a nontrivial UV fixed point at leading order in $1/N_f$ suggests the possibility of asymptotic safety, the absence of higher-order terms precludes robust conclusions. We analyze the impact of renormalization scheme transformations and show that higher-order corrections inevitably introduce increasingly singular contributions. We prove that at most one renormalization scheme can preserve the dominance of the leading contribution, rendering the truncation trustworthy; in all other schemes, higher-order terms dominate and the expansion becomes unreliable. This result places strong constraints on the physical interpretation of UV fixed points in large $N_f$ theories and emphasizes the need for resummation or non-perturbative control to establish asymptotic safety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probing Large $N_f$ Through Schemes Pinoy, Alan Vatani, Shahram High Energy Physics - Phenomenology High Energy Physics - Theory We investigate the reliability of the large $N_f$ expansion of four-dimensional gauge-fermion quantum field theories, focusing on the structure and scheme dependence of the beta function. While the existence of a nontrivial UV fixed point at leading order in $1/N_f$ suggests the possibility of asymptotic safety, the absence of higher-order terms precludes robust conclusions. We analyze the impact of renormalization scheme transformations and show that higher-order corrections inevitably introduce increasingly singular contributions. We prove that at most one renormalization scheme can preserve the dominance of the leading contribution, rendering the truncation trustworthy; in all other schemes, higher-order terms dominate and the expansion becomes unreliable. This result places strong constraints on the physical interpretation of UV fixed points in large $N_f$ theories and emphasizes the need for resummation or non-perturbative control to establish asymptotic safety. |
| title | Probing Large $N_f$ Through Schemes |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.16504 |