 Composite Kähler connection

The scalar fields of chiral matter induce a composite phase connection proportional to $i(K_i{\partial }_{\mu }{z}^i-K_{\bar{i}}{\partial }_{\mu }{\bar{z}}^{\bar{i}})$. For canonical Kähler potential it is proportional to the scalar phase current. The chiral matter fermions and gravitino have appropriate Kähler weights; expanding their connection terms produces scalar-current–fermion-bilinear couplings. Overall signs and coefficients depend on spinor and Planck-scale conventions.