The Effective Kahler Potential, Metastable Vacua and R-Symmetry Breaking in O'Raifeartaigh Models

Much has been learned about metastable vacua and R-symmetry breaking in O'Raifeartaigh models. Such work has largely been done from the perspective of the superpotential and by including Coleman-Weinberg corrections to the scalar potential. Instead, we consider these ideas from the perspective of the one loop effective K\"ahler potential. We translate known ideas to this framework and then construct convenient formulas for computing individual terms in the expanded effective K\"ahler potential. We do so for arbitrary R-charge assignments and allow for small R-symmetry violating terms so that both spontaneous an explicit R-symmetry breaking is included in our analysis.