Finite Nonlocal Holomorphic Unified Quantum Field Theory (2507.14203v1)

Abstract: In this paper the non-local finite quantum-gravity framework is incorporated into the Complex non-Riemannian Holomorphic Unified Field Theory formulated on a complexified four-dimensional manifold. By introducing entire-function regulators $F(\Box) = \exp!\bigl(\Box / M_*^2\bigr)$ into the holomorphic Einstein-Hilbert action, we achieve perturbative UV finiteness at all loop orders, while preserving BRST invariance and holomorphic gauge symmetry. We derive the modified gauge-gravity coupling sector, perform a one-loop effective-action computation in a contour-regularized metric background, and demonstrate the absence of new counterterms and problematic complex-pole structures. Extending the construction to nontrivial curved backgrounds, we verify infrared recovery of General Relativity and full holomorphic gauge invariance. Finally, we explore phenomenological consequences, including corrected graviton and gauge-boson scattering amplitudes in self-dual backgrounds, finite Hawking spectra for regularized Schwarzschild and Kerr geometries, and proposed tests of the equivalence principle. This work lays the foundation for a self-consistent, unitary four-dimensional quantum-gravity and Holomorphic Unified Field Theory framework.