Metastable SUSY Breaking and Supergravity at Finite Temperature

We study how coupling to supergravity affects the phase structure of a system exhibiting dynamical supersymmetry breaking in a metastable vacuum. More precisely, we consider the Seiberg dual of SQCD coupled to supergravity at finite temperature. We show that the gravitational interactions decrease the critical temperature for the second order phase transition in the quark direction, that is also present in the global case. Furthermore, we find that, due to supergravity, a new second order phase transition occurs in the meson direction, whenever there is a nonvanishing constant term in the superpotential. Notably, this phase transition is a necessary condition for the fields to roll, as the system cools down, towards the metastable susy breaking vacuum, because of the supergravity-induced shift of the metastable minimum away from zero meson vevs. Finally, we comment on the phase structure of the KKLT model with uplifting sector given by the Seiberg dual of SQCD.