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arXiv · 2512.02123

General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions

York Schröder·Emmanuel Stamou·Tom Steudtner·Max Uetrecht
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Abstract

We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations between the template RGE coefficients, valid in any renormalisation scheme. Directly in $d=3$, we identify a new theory with a non-trivial IR fixed point that is under perturbative control in a large-$N$ limit. We provide up-to-date numerical results for all required massive tadpole master integrals up to four loops and complement them with analytic expressions where available.

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York Schröder, Emmanuel Stamou, Tom Steudtner, Max Uetrecht. 2025-12-01. General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions. https://doi.org/10.21468/scipostphys.20.6.168

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