General four-loop beta function for scalar-fermion theories in three dimensions

We present general four-loop template \beta β -functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing \mathcal{N}=1 𝒩 = 1 and \mathcal{N}=2 𝒩 = 2 supersymmetry, we obtain relations between the template RGE coefficients, valid in any renormalisation scheme. Directly in d=3 d = 3 , we identify a new theory with a non-trivial IR fixed point that is under perturbative control in a large- N 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.