Supergravity auxiliary field ($F^i=-e^{K/2}{K}^{i\bar{j}}\overline{D_{j}W}$)

After eliminating the chiral auxiliary fields in Planck-unit supergravity, one convention gives $F^i=-e^{K/2}{K}^{i\bar{j}}\overline{D_{j}W}$. The upper-index inverse satisfies $K_{i\bar{j}}{K}^{k\bar{j}}={\delta }_i^k$. Nonzero auxiliary expectation values diagnose supersymmetry breaking; their common phase convention does not affect the vanishing condition.