Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models

TL;DR

The paper develops two manifest-SUSY frameworks to study BPS domain walls in four-dimensional ${ m N}=2$ nonlinear sigma models with hyper-Kähler targets. It first constructs massive HK sigma models on $T^*CP^n$ via a massive HK quotient in ${ m N}=1$ language, and then provides a harmonic superspace (HSF) formulation that preserves all SUSY; both approaches yield BPS wall equations and explicit wall solutions for the $n=1$ case. The BPS structures arise from the norm of tri-holomorphic Killing vectors and FI/mass deformations, with the EH geometry providing a concrete realization and a CP^1 reduction that matches known results. The work also analyzes zero-mode dynamics and the low-energy effective action on walls, highlighting three-dimensional Lorentz invariance on the wall worldvolume and offering a robust SUSY-consistent framework for domain walls in ${ m N}=2$ sigma models. Overall, it establishes a consistent, dual formulation for BPS walls in HK-target theories and lays groundwork for LEEA analyses and brane-world applications.

Abstract

BPS equations and wall solutions are studied keeping (part of) supersymmetry (SUSY) manifest. Using N=1 superfields, massive hyper-Kahler quotient is introduced to obtain massive N=2 (8 SUSY) nonlinear sigma models in four dimensions with T*CP(n) target manifold, which yield BPS wall solutions for the n=1 case. We also describe massive hyper-Kahler quotient of T*CP(n) by using the harmonic superspace formalism which preserves all SUSY manifestly, and BPS equations and wall solutions are obtained in the n=1 case.