Supersymmetry and R-symmetry breaking in metastable vacua at finite temperature and density

We study a metastable supersymmetry-breaking vacuum in a generalized O'Raifeartaigh model at finite temperature and chemical potentials. Fields in the generalized O'Raifeartaigh model possess different R-charges to realize R-symmetry breaking. Accordingly, at finite density and temperature, the chemical potentials have to be introduced in a nonuniform way. Based on the formulation elaborated in our previous work, we study the one-loop thermal effective potential including chemical potentials in the generalized O'Raifeartaigh model. We perform a numerical analysis and find that the R-symmetry-breaking vacua, which exist at zero temperature and zero chemical potential, are destabilized for some parameter regions. In addition, we find that there are parameter regions where new R-symmetry-breaking vacua are realized even at high temperature by the finite density effects.