From Non-Abelian Vortex Strings to Discrete Vorton Dynamics: Moduli Reduction, Representation Boundaries, and Topological Dissipation

We establish the mathematical correspondence between non-Abelian vortex strings in supersymmetric gauge theories and discrete vorton networks in three-dimensional hydrodynamics.
In continuous field theory, apparent ultraviolet divergences are regularized when physical degrees of freedom are restricted to a reduced configuration space: non-Abelian strings in N = 2 supersymmetric gauge theories avoid singular core collapse because their internal orientations parameterize a compact K¨ahler coset space (CPN−1), while adiabatic metric contraction (ϵ2 → 0) of Yang–Mills theory on Σ2 × T2p forces internal curvature freeze-out (F0ij = 0), projecting four-dimensional gauge fields onto the moduli space of flat connections.
We demonstrate that the discrete vorton framework provides a hydrodynamic realization of this reduction principle, replacing continuous field divisibility with an irreducible lattice scale ℓv. We resolve all open conjectures into rigorous mathematical theorems.