Charge Spin Separation in 3D

Electron fractionalization into spinons and chargeons plays a crucial role in 2D models of strongly correlated electrons. In this paper we show that spin-charge separation is not a phenomenon confined to lower dimensions but, rather, we present a field-theoretic model in which it is realized in 3D. The model involves two gauge fields, a standard one and a two-form gauge field. The physical picture is that of a two-fluid model of chargeons and spinons interacting by the topological BF term. When a Higgs mechanism of the second kind for the two-form gauge field takes place, chargeons and spinons are bound together into a charge 1 particle with spin 1/2. The mechanism is the same one that gives spin to quarks bound into mesons in non-critical string theories and involves the self-intersection number of surfaces in 4D space-time. A state with free chargeons and spinons is a topological insulator. When chargeons condense, the system becomes a topological superconductor; a condensate of spinons, instead realizes U(1) charge confinement.