General 2+1 Dimensional Effective Actions and Soliton Spin Fractionalization

TL;DR

This paper develops a general framework for 2+1 dimensional non-linear sigma models with Chern-Simons terms, revealing how soliton spins fractionalize based on topological charges and couplings, extending previous models to more complex cosets.

Contribution

It introduces the most general non-linear sigma model actions with Chern-Simons terms on cosets G/H, demonstrating soliton spin fractionalization for multiple topological charges and generalizing earlier models.

Findings

Multiple topological charges lead to distinct conserved quantities.

Soliton spins fractionalize as functions of Chern-Simons couplings.

Model generalizes Wilczek-Zee soliton spin fractionalization to arbitrary G/H.

Abstract

We propose actions for non-linear sigma models on cosets $G/H$ in 2+1 dimensions that include the most general non-linear realizations of Chern-Simons terms. When $G$ is simply connected and $H$ contains $r$ commuting U(1) factors, there are $r$ different topologically conserved charges and generically $r$ different types of topological solitons. Soliton spin fractionalizes as a function of the Chern-Simons couplings, with independent spins associated to each species of soliton charge, as well as to pairs of different charges. This model of soliton spin fractionalization generalizes to arbitrary $G/H$ a model of Wilczek and Zee for one type of soliton.