Anyonic vortex line states in 3+1d interacting Bose systems.

In this talk, I will propose a generalization of the Chern-Simons (CS) transformation for hard-core interacting Bosons in 3+1d space-time. This method combines ordinary (CS) transformation in 2+1 dimensions and 1D Jordan-Wigner fermionization along an arbitrary vortex line. There are two possible approaches to define the action. One way is to introduce a new metric on transversal to vortices planes with varying z-coordinates connected by area-preserving diffeomorphisms. The action contains a new term different from a usual Chern-Simons action and differs from the BF-like term. The second approach focuses on the flat metric, and the transformation yields a new action for the emergent matter fields coupled to an emergent U(1) gauge field. We discuss the connection between the two field theories and look at the low energy limit when two approaches yield the same result. We apply the obtained results to 3D interacting Bose systems with an infinitely degenerate moat-like single-particle dispersion. We argue that these systems exhibit an absence of condensation and stabilize ground states with anyonic vortices with non-trivial braiding and fusion rules.