O(3) Non-linear $σ$ model with Hopf term and Higher spin theories

Abstract

Following our earlier work we argue in detail for the equivalence of the nonlinear $σ$ model with Hopf term at~$θ=π/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $σ$ model and show the equivalence of the correlation functions.We also show the relation between topological and Noether currents. We obtain the Lorentz and discrete transformation properties of the spin-s operator from the fields of the $σ$ model. We also explore the connection of this model with Quantum Hall Fluids.