Bifold Quantum Gravity: Spacetime under the CPT Constraint, Gauge Coupling Running, and Ultraviolet/Infrared Completeness

Abstract

Starting from the group-theoretic realization of the CPT theorem, we establish the Bifold quantum gravity framework. CPT, as an antiunitary operator, exchanges the two $SU(2)$ factors of the complexified Lorentz algebra, constituting the binary structure of dual-SU(2) spacetime. The algebraic structure of dual SU(2) gives noncommutative geometry, whose equivalent physical description is compactification. From this we derive C_\pm dynamics. Within this framework, we compute the one-loop running of the gauge coupling and, under the boundary conditions \mu_0=M_P/(8\pi) and g_2^2(\mu_0)=1, obtain an infrared Landau pole at 7.4 TeV. The compact cutoff of the rotation sector makes all momenta discrete, turning loop integrals into finite sums and proving ultraviolet completeness; the minimum momentum provides an infrared cutoff and proves infrared completeness. Within this framework, we obtain a rigorous solution to the strong CP problem, \bar\theta=0, consistent with the experimental constraint |\bar\theta|<10^{-10}. The framework further yields two conditional predictions: the Landau pole as the gravitational microscopic scale, and the discrete gauge-coupling energy scales. Bifold quantum gravity provides a ultraviolet- and infrared-complete quantum gravity framework that matches experiments and has testable predictions.