Four Loop Renormalisation Group Equations in general Gross-Neveu-Yukawa Theories

Abstract: We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel contributions to the $\beta$-functions of the Higgs and top coupling are extracted. We discuss how four loops present a challenge to dimensional continuation from four to three dimensions and propose a solution.