Topological Fermions from Framed Vortex Loops in a Quantized Superfluid Effective Field Theory (v5) Part I

AbstractWe present an emergent hydrodynamic framework for fermionic statistics within a 3 + 1-dimensional quantized superfluid effective field theory (EFT). While classical vortices in irrotational fluids are bosonic, we demonstrate that quantized vortex loops generically acquire an effective internal framing arising from the anisotropic geometry and phase-gradient structure of their cores. These framed vortex loops inhabit a configuration space C ∼= (T³ × SO (3) ) N /SN. We define the Berry connection on the Hilbert bundle of condensate states and show that the adiabatic exchange of two such defects corresponds to a non-contractible loop in SO (3). Due to π1 (SO (3) ) ∼= Z2, the resulting holonomy yields a topological phase π, producing the fermionic exchange sign eⁱπ = −1. This provides a concrete mechanical realization of the Finkelstein–Rubinstein constraint and suggests that half-integer spin and fermionic statistics emerge as topological properties of a superfluid vacuum.