R-symmetry and Supersymmetry Breaking at Finite Temperature

We analyze the spontaneous $U(1)_R$ symmetry breaking at finite temperature for the simple O'Raifeartaigh-type model introduced in [1] in connection with spontaneous supersymmetry breaking. We calculate the finite temperature effective potential (free energy) to one loop order and study the thermal evolution of the model. We find that the R-symmetry breaking occurs through a second order phase transition. Its associated meta-stable supersymmetry breaking vacuum is thermodynamically favored at high temperatures and the model remains trapped in this state by a potential barrier, as the temperature lowers all the way until T=0.