Gradient RG Flow in Scalar-Fermion QFTs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908626152587264 |
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| author | Pannell, William H. Ronayne, William Patrick Stergiou, Andreas |
| author_facet | Pannell, William H. Ronayne, William Patrick Stergiou, Andreas |
| contents | The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in $d=4$ and $d=4-\varepsilon$ dimensions. The crucial role played by the beta shift, which is a modification of the standard dim-reg beta function, is elucidated, and specific conditions that it needs to satisfy for the RG flow to be gradient are derived. Over a thousand gradient-flow conditions are found, all of which are scheme-independent and satisfied whenever the full set of results needed to check them is available. It is shown, in the framework of the $\varepsilon=4-d$ expansion, that the space of conformal field theories (CFTs) is dominated by those with non-zero beta shift as the number of fields grows. Physical properties of CFTs obtained as solutions where the beta functions are not zero in the $\varepsilon$ expansion are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient RG Flow in Scalar-Fermion QFTs Pannell, William H. Ronayne, William Patrick Stergiou, Andreas High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in $d=4$ and $d=4-\varepsilon$ dimensions. The crucial role played by the beta shift, which is a modification of the standard dim-reg beta function, is elucidated, and specific conditions that it needs to satisfy for the RG flow to be gradient are derived. Over a thousand gradient-flow conditions are found, all of which are scheme-independent and satisfied whenever the full set of results needed to check them is available. It is shown, in the framework of the $\varepsilon=4-d$ expansion, that the space of conformal field theories (CFTs) is dominated by those with non-zero beta shift as the number of fields grows. Physical properties of CFTs obtained as solutions where the beta functions are not zero in the $\varepsilon$ expansion are discussed. |
| title | Gradient RG Flow in Scalar-Fermion QFTs |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.01971 |