Fermions and the Renormalisation Group at Large N
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arXiv
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| Format: | Preprint |
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2025
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| author | Cresswell-Hogg, Charlie Litim, Daniel F. |
| author_facet | Cresswell-Hogg, Charlie Litim, Daniel F. |
| contents | We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local interaction functionals of fermion bilinears. The structure implies that local potential approximations are exact, exactly solvable, and that field anomalous dimensions vanish. Theories with non-trivial anomalous dimensions may also arise under conditions that are identified. We further demonstrate that higher derivative interactions are inevitably induced by point-like ones, including at large-$N$. The local potential flows for fermionic theories with the most general $U(N)$ symmetric interactions are provided. For sample theories with scalar, pseudo-scalar, vector, or axial-vector interactions, we identify conformal fixed points, scaling dimensions, conformal manifolds, and quantum-induced shifts in scaling dimensions of higher derivative interactions. We also study fermion mass generation, and subleading modifications due to finite $N$ corrections. Implications for conformal field theories, and applications in condensed matter and particle physics are indicated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fermions and the Renormalisation Group at Large N Cresswell-Hogg, Charlie Litim, Daniel F. High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local interaction functionals of fermion bilinears. The structure implies that local potential approximations are exact, exactly solvable, and that field anomalous dimensions vanish. Theories with non-trivial anomalous dimensions may also arise under conditions that are identified. We further demonstrate that higher derivative interactions are inevitably induced by point-like ones, including at large-$N$. The local potential flows for fermionic theories with the most general $U(N)$ symmetric interactions are provided. For sample theories with scalar, pseudo-scalar, vector, or axial-vector interactions, we identify conformal fixed points, scaling dimensions, conformal manifolds, and quantum-induced shifts in scaling dimensions of higher derivative interactions. We also study fermion mass generation, and subleading modifications due to finite $N$ corrections. Implications for conformal field theories, and applications in condensed matter and particle physics are indicated. |
| title | Fermions and the Renormalisation Group at Large N |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2502.04473 |