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

TL;DR

This paper demonstrates the equivalence between a non-linear sigma model with a Hopf term at specific angles and an interacting higher spin theory, revealing deep connections with topological currents and quantum Hall systems.

Contribution

It provides a detailed ansatz for spin-s operators in the sigma model and establishes their correlation functions and transformation properties, linking topological and Noether currents.

Findings

Equivalence of sigma model with Hopf term and spin-s theory at specific angles

Explicit form of spin-s operators and their correlation functions

Connection to quantum Hall fluid phenomena

Abstract

Following our earlier work we argue in detail for the equivalence of the nonlinear $\sigma$ model with Hopf term at~$\theta=\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\sigma$ 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 $\sigma$ model. We also explore the connection of this model with Quantum Hall Fluids.