Four Fermi Theory in Four Dimensions is Renormalisable
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908910292566016 |
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| author | Cresswell-Hogg, Charlie Litim, Daniel F. |
| author_facet | Cresswell-Hogg, Charlie Litim, Daniel F. |
| contents | We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying divergence structure and using Gross-Neveu-type interactions as a template, we explain why extended four-fermion theories including higher-derivative interactions are well-defined, renormalisable, and predictive with only a few free parameters. We also provide the exact large-$N_{\rm f}$ leading beta functions of couplings and discuss quantum scaling dimensions, universality, $1/N_{\rm f}$ corrections, and extensions to other types of four fermion interactions. Implications for effective theory and model building are indicated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19357 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Four Fermi Theory in Four Dimensions is Renormalisable Cresswell-Hogg, Charlie Litim, Daniel F. High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying divergence structure and using Gross-Neveu-type interactions as a template, we explain why extended four-fermion theories including higher-derivative interactions are well-defined, renormalisable, and predictive with only a few free parameters. We also provide the exact large-$N_{\rm f}$ leading beta functions of couplings and discuss quantum scaling dimensions, universality, $1/N_{\rm f}$ corrections, and extensions to other types of four fermion interactions. Implications for effective theory and model building are indicated. |
| title | Four Fermi Theory in Four Dimensions is Renormalisable |
| topic | High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2603.19357 |