On the Invariant and Geometric Structure of the Holomorphic Unified Field Theory

Abstract

We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and curvature equipped with a Hermitian field on a complexification of spacetime. From a single $\mathrm{Diff}(M)\times G$-invariant action, variation yields the Einstein and Yang-Mills equations together with their paired Bianchi identities. A compatibility condition is implemented either definitionally or through an auxiliary penalty functional. It enforces that the antisymmetric part of our Hermitian field is the gauge field's exact curvature on the real slice.