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arXiv · 2502.04473

Fermions and the Renormalisation Group at Large N

Charlie Cresswell-Hogg·Daniel F. Litim
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Abstract

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.

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Charlie Cresswell-Hogg, Daniel F. Litim. 2025-02-06. Fermions and the Renormalisation Group at Large N. https://arxiv.org/abs/2502.04473

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