Four loop renormalisation group equations in general Gross-Neveu-Yukawa theories

A bstract We compute template formulae of all four-loop β -functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme. Using these results, novel contributions to the β -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.