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

Abstracts:

We present general four-loop template β-functions and anomalous field dimensions for renormalizable scalar-fermion theories in three dimensions. By imposing N = 1 and N = 2 supersymmetry, we obtain relations between the template RGE coefficients, valid in any renormalization 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.

Link to the paper:

https://arxiv.org/abs/2512.02123