Probing Large $N_f$ Through Schemes

Alan Pinoy; Shahram Vatani

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arXiv · 2507.16504

Probing Large $N_f$ Through Schemes

Alan Pinoy·Shahram Vatani

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Abstract

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.

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Alan Pinoy, Shahram Vatani. 2025-07-22. Probing Large $N_f$ Through Schemes. https://arxiv.org/abs/2507.16504

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