Topological field configurations in the presence of isospin chemical potential

We analyze the stability of different topological solutions in quantum field theory when an isospin chemical potential μ is included. We work in the limit when temperature vanishes. We find that static vortex solutions in 2+1D do exist. However, the 't Hooft-Polyakov monopole in 3+1D is no longer stable, as soon as the chemical potential acquires a finite value. In the case of the skyrmion, this topological solution still exists for finite μ, up to a certain critical value.