Renormalization of vacuum expectation values in spontaneously broken gauge theories

Understand

We compute one-loop and two-loop beta-functions for vacuum expectation values (VEVs) in gauge theories.

• In R_xi gauge the VEVs renormalize differently from the respective scalar fields.
• We focus particularly on the origin and behavior of this difference and show that it can be interpreted as the anomalous dimension of a certain scalar background field, leading to simple direct computation and qualitative understanding.
• The results are given for generic as well as supersymmetric gauge theories.