  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.
