Abstract

We present the complete quantum field theory of Distortion Gravity (DG), a metric-affine extension of General Relativity in which the affine connection carries independent dynamics. Starting from the ghost-free classical action—proven unitary via Dirac-Bergmann analysis, polarization completeness, and 290,000 numerical tests—we perform the full canonical quantization of the two massive vector fields \(V_{\mu}\) (trace non-metricity) and \(a_{\mu}\) (axial torsion). We derive the complete set of Feynman rules, including all graviton-vector and vector self-interaction vertices. Using the DeWitt-Seeley heat-kernel expansion, we compute the one-loop beta functions for the Newton constant \(G_{N}\), the Proca masses \(m_{V}^{2}, m_{a}^{2}\), and the distortion invariants \(\alpha_{1}, \alpha_{2}, \alpha_{3}\), providing all numerical coefficients explicitly. The renormalization group equations admit a non-trivial ultraviolet fixed point with \(\tilde{G}_{N}^{*} \simeq 0.118\), indicating that the theory is asymptotically safe. We compute the quantum corrections to the cosmological constant, predicting \(\rho_{\mathrm{vac}} \sim 10^{-47} \mathrm{GeV}^{4}\) without fine-tuning. We derive the logarithmic corrections to the Bekenstein-Hawking entropy and to the Hawking temperature, and we show that the circular polarization of Hawking radiation from Green holes receives a calculable running. We verify that the induced fission of \(^{12}\mathrm{C}\), \(^{16}\mathrm{O}\), and \(^{56}\mathrm{Fe}\) via axial torsion remains robust under quantum corrections. Finally, we address the foundational implications: the dynamical resolution of the problem of time, the exact realization of \(\mathrm{ER} = \mathrm{EPR}\) through the quantized axial flux, and the emergence of decoherence from torsion-matter interactions. The theory is renormalizable, unitary, and predictive, providing a complete framework for quantum gravity that is experimentally accessible in the coming decade.