On the Gauged Non-compact Spin System

TL;DR

This paper explores a non-compact spin system coupled with Chern-Simons gauge fields, revealing finite-energy solitons, connections to known models in certain limits, and its realization as an anyon field theory.

Contribution

It introduces a classical non-compact spin model with finite-energy solitons and analyzes its quantum properties, linking it to known gauge theories and anyon physics.

Findings

Existence of finite-energy Bogomol'nyi solitons.

Reduction to gauged nonlinear Schrödinger or Abelian Higgs models in large spin limit.

Quantum spin algebra exhibits anomalous commutation relations, indicating anyonic behavior.

Abstract

We examine classical and quantum aspects of the planar non-compact spin system coupled with Chern-Simons gauge field in the presence of background charge. We first define our classical spin system as non- relativistic non-linear sigma model in which the order parameter spin takes value in the non-compact manifold ${\cal M}=SU(1,1)/U(1)$. Although the naive model does not allow any finite energy self dual solitons, it is shown that the gauged system admits static Bogomol'nyi solitons with finite energy whose rotationally symmetric soliton solutions are analyzed in detail. We also discuss the large spin limit in which the self-dual equation reduces to the well-known gauged non- linear Schr\"odinger model or Abelian Higgs model, depending on the choice of the background charge term. Then, we perform quantization of the model. We find that the spin algebra satisfies anomalous commutation relations, and the system is a field theoretic realization of the anyons.