General Kähler potential including chiral matter

Develop a general expression for the four-dimensional N=1 Kähler potential that includes the Kähler metrics of all chiral matter superfields arising in large-volume string compactifications (such as heterotic compactifications on Calabi–Yau threefolds and Type II orientifolds), so that physical Yukawa couplings can be computed systematically across generic models.

Background

In four-dimensional N=1 string compactifications, physical Yukawa couplings are determined by the superpotential and the Kähler potential, with the latter encoding the Kähler metrics of chiral fields. While holomorphic superpotential terms can sometimes be computed using advanced techniques, obtaining Kähler metrics for chiral matter is generally more difficult beyond simple setups.

A general, model-independent Kähler potential incorporating all chiral fields would enable systematic and reliable computation of physical Yukawas, but such an expression has not yet been established.