= 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.
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