Supersymmetric Intersecting Domain Walls in Massive Hyper-Kahler Sigma Models

TL;DR

The paper analyzes massive HK sigma models with eight supercharges in D=3,4 and shows that, beyond standard 1/2-BPS domain walls, there exist exact 1/4-BPS intersections of domain walls when the HK target has at least two commuting tri-holomorphic KVFs. The general scalar potential is shown to be the sum of squares of these KVFs, and in toric HK 8-manifolds the potential takes the form V = 1/2 μ^2_{IJ} U^{IJ}, with μ^2 of rank 2; this permits nontrivial static intersections. By including a third KVF one obtains 1/4-BPS stationary charged intersections, corresponding to waves along the intersection, and dimensional reduction to D=3 yields charged intersecting walls in a D=3 model. The results are connected to D1-D5 brane physics and suggest broader applicability to Calabi manifolds, highlighting new supersymmetric solitons in higher-dimensional HK target spaces and their physical interpretations.

Abstract

The general scalar potential of D-dimensional massive sigma-models with eight supersymmetries is found for $D=3,4$. These sigma models typically admit 1/2 supersymmetric domain wall solutions and we find, for a particular hyper-Kähler target, exact 1/4 supersymmetric static solutions representing a non-trivial intersection of two domain walls. We also show that the intersecting domain walls can carry Noether charge while preserving 1/4 supersymmetry. We briefly discuss an application to the D1-D5 brane system.