In this talk, I will introduce the concept of renormalization group flow and describe the general features that can be found in such flows in (gauge-)Yukawa theories. In perturbation theory, the renormalization group flow is given by the beta functions of the various couplings, and these can be calculated to different loop orders. It will become apparent that it is necessary to have a criterion that can determine the correct way to go to higher order in the multi-coupling loop expansion. I propose that the Weyl consistency conditions are exactly that criterion and present both their derivation and their implication. If there is sufficient time, I will also touch upon how this affects the stability of the standard model vacuum.

Oleg Antipin, Marc Gillioz, Jens Krog, Esben Mølgaard, and Francesco Sannino, Standard Model Vacuum Stability and Weyl Consistency Conditions," JHEP 1308, 034 (2013), arXiv:1306.3234 [hep-ph] Esben Mølgaard and Robert Shrock, "Renormalization-Group Flows and Fixed Points in Yukawa Theories," Phys.Rev. D, accepted for publication (2014), arXiv:1403.3058 [hep-th]