R-symmetry Breaking and O'Raifeartaigh Model with Global Symmetries at Finite Temperature

We investigate finite temperature effects in O'Raifeartaigh models with global symmetries which exhibit supersymmetry breaking at a meta-stable vacuum accompanied by $U(1)_R$ breaking. The pseudo moduli field is stabilized at one-loop order at zero temperature within some coupling parameter region. We analyze the behavior of the parameter space according to non-zero temperatures and find that the parameter region which allows $U(1)_R$ breaking is considerably extended at sufficiently low temperature, even though it shrinks down at high temperature as expected. We also discuss the thermal history of the meta-stable supersymmetry breaking vacuum.