One-loop functional renormalization group flow of scalar theories with electroweak symmetry

Using functional renormalization methods, we study the one-loop renormalization group evolution of theories with four scalars, at second order in the derivative expansion, in which electroweak symmetry is nonlinearly realized. In this framework we study the stability of $O(4)$ symmetry and find the $O(4)$-violating eigenperturbations and their corresponding eigenspectrum around three different geometries of the target space, namely those of the flat space, cylinder, and sphere.