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

TL;DR

This paper derives four-loop beta functions for scalar-fermion theories in three dimensions, revealing a new IR fixed point under supersymmetry constraints and providing detailed numerical and analytic results for related integrals.

Contribution

It provides the first four-loop beta functions and anomalous dimensions for three-dimensional scalar-fermion theories, including supersymmetry relations and a new IR fixed point.

Findings

Identified a new non-trivial IR fixed point in three dimensions.

Provided comprehensive four-loop numerical results for master integrals.

Established relations between RG coefficients under supersymmetry constraints.

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.