Skyrme model and isospin chemical potential

We discuss the stability of the skyrmion solution in the presence of a finite isospin chemical potential μ. Solving numerically the mass of the skyrmion as function of μ, we find a critical value μc=222.8MeV where the skyrmion mass vanishes. We compare the exact numerical treatment with an analytical discussion based on a special shape for the profile of the skyrmion due to Atiyah and Manton. The extension of this ansatz for finite μ works quite well for μ<121MeV. Then, for small values of μ, where the analytical approach is valid, we consider the possibility of having an angular deformation for the skyrmionic profile, which is possible for finite values of μ. This is, however, a small effect. Finally we introduce finite temperature corrections, which strength the instability induced by the chemical potential, finding the dependence of the critical temperature on μ