Finite Nonlocal Holomorphic Unified Quantum Field Theory

TL;DR

This paper develops a finite, perturbatively UV-complete quantum gravity theory within a holomorphic unified field framework, incorporating nonlocal regulators to preserve gauge invariance and avoid divergences.

Contribution

It introduces entire-function regulators into a holomorphic Einstein-Hilbert action, achieving UV finiteness at all loop orders while maintaining gauge symmetry and BRST invariance.

Findings

Demonstrates perturbative UV finiteness and absence of new counterterms.

Shows infrared recovery of General Relativity and gauge invariance.

Explores phenomenological implications like modified scattering amplitudes and Hawking spectra.

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.