Massive Nonlinear Sigma Models and BPS Domain Walls in Harmonic Superspace

TL;DR

This paper explores massive N=2 nonlinear sigma models and BPS domain wall solutions using harmonic superspace, focusing on hyper-Kahler target spaces like Taub-NUT and Eguchi-Hanson, revealing domain walls only in the double Taub-NUT case.

Contribution

It introduces a harmonic superspace formulation for massive N=2 sigma models with hyper-Kahler targets and derives BPS equations for specific metrics, identifying conditions for domain wall existence.

Findings

Domain walls exist only in the double Taub-NUT case.

The harmonic potential generalizes Kahler potential to N=2 theories.

Explicit BPS equations are derived for Taub-NUT and Eguchi-Hanson limits.

Abstract

Four-dimensional massive N=2 nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which N=2 supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kahler analog of the Kahler potential in N=1 theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kahler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi-Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi-Hanson limit.