Noncommutative field theory description of quantum Hall skyrmions

TL;DR

This paper employs noncommutative field theory to analyze quantum Hall skyrmions at filling factor one, deriving BPS conditions, moduli space dimensions, and effective models, providing new insights into their structure and interactions.

Contribution

It introduces a noncommutative field theory framework to study quantum Hall skyrmions, deriving BPS bounds, moduli space dimensions, and effective Lagrangians, which are novel contributions.

Findings

Multi-skyrmions saturate BPS bounds.

Moduli space dimension for k skyrmions is 4k+2.

Effective nonlinear sigma model is derived.

Abstract

We revisit the quantum Hall system with no Zeeman splitting energy using the noncommutative field theory. We analyze the BPS condition for the delta-function interaction near the filling factor $\nu=1$. Multi-skyrmions are shown to saturate the BPS bounds. The dimension of the moduli space of $k$ skyrmions is $4k+2$. Advantage of the noncommutative field description is demonstrated through the derivation of the effective nonlinear $\sigma$ model Lagrangian.