SciPost Submission Page
General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions
by York Schröder, Emmanuel Stamou, Tom Steudtner, Max Uetrecht
Submission summary
| Authors (as registered SciPost users): | Max Uetrecht |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202512_00026v1 (pdf) |
| Date submitted: | Dec. 10, 2025, 2:45 p.m. |
| Submitted by: | Max Uetrecht |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
ChatGPT 5: Minor text polishing
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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