Quantum Vortex Theory: Topology, Defects and Emergent Transport

This work presents a minimal and self-consistent formulation of Quantum Vortex Theory (QVT) based on a compact phase field. Starting from first principles, we establish a closed logical chain linking phase structure, topological obstruction, defect formation, coherence breakdown, and emergent transport. We show that transport is not an additional phenomenon but a necessary consequence of phase topology. Quantized circulation enforces the existence of defects as localized carriers of topological charge. These defects are not optional excitations but structurally required objects that mediate all nontrivial transport. A local structural indicator based on phase curvature is introduced to characterize the transition between coherent and activated regimes. This leads to an effective transport law in which defect motion, activated by curvature, generates macroscopic flow. The resulting framework is minimal, local, and contains no auxiliary fields. It establishes defect-mediated transport as the only mechanism compatible with compact phase structure and topological consistency. This paper provides the foundational formulation of QVT. A fully predictive dynamical completion based on a variational principle is developed in subsequent work.