Consider a chiral fermion flavor symmetry, $U(3)_L\otimes U(3)_R$, such as the flavor symmetry of the approximately massless up, down, and strange quarks. In QCD, this symmetry is spontaneously broken down to $U(3)_V$. Now let us assume that the symmetry $U(3)_L\otimes U(3)_R$ could get completely broken down to $U(1)\otimes U(1)\otimes U(1)$ (from which one axial $U(1)$ symmetry is anomalous).
What kinds of topological defects would we expect? Strings and domain walls will be created, if the anomalous axial $U(1)$ symmetry is explicitly broken down to $Z_N$ and $Z_N$ is spontaneously broken down to nothing, similar to what happens in QCD axion scenarios. But what other topological defects will emerge when breaking the entire large symmetry group? Textures, monopoles, or even more?