Topology

Torsion, Topology, and Fermions: A Synthesis of Canonical, Covariant, and Asymptotically Safe Quantum Gravity

Authors: Justin Sirotin
Comments: 25 Pages. (Note by ai.viXra.org Admin: Please use standard math/equation/formula typesetting such as LaTeX)

This report provides a comprehensive synthesis of contemporary approaches to incorporating fermionic matter into non-perturbative quantum gravity. We begin by establishing the foundational role of the Nieh-Yan topological density in the first-order gravitational action, demonstrating its connection to the Barbero-Immirzi parameter and its implications for parity symmetry. We then perform a detailed canonical analysis of the Einstein-Cartan-Holst-Dirac system within the Loop Quantum Gravity (LQG) framework, elucidating how fermions source spacetime torsion, deform the symplectic structure, and introduce profound coupling ambiguities. The covariant perspective is explored through the spinfoam formalism, where we describe a minimal coupling for fermions as excitations on the boundaries of quantum spacetime, ensuring consistency with the canonical picture. Finally, we investigate the Asymptotic Safety paradigm as a potential mechanism for ultraviolet completion, focusing on the functional renormalization group flow of Einstein-Cartan theory. We argue that torsion acts as a unifying physical concept across these formalisms and that the principle of Asymptotic Safety may provide a physical selection criterion to resolve the ambiguities inherent in the canonical theory. The analysis reveals that a fundamental parity violation may be a generic prediction of quantum gravity coupled to the Standard Model.
Category: Topology