Sigma-model soliton intersections from exceptional calibrations

TL;DR

This paper derives BPS equations for supersymmetric soliton intersections in sigma models, finds explicit solutions preserving partial supersymmetry, and links these to calibrated geometries, advancing understanding of soliton interactions in higher-dimensional theories.

Contribution

It introduces new first-order BPS equations for soliton intersections in supersymmetric sigma models and connects them to calibrated geometries, providing explicit solutions and supersymmetry preservation analysis.

Findings

Derived BPS equations for 1/8 and 1/4 supersymmetric soliton intersections.

Found explicit non-singular solutions preserving 1/4 supersymmetry.

Linked BPS equations to Cayley calibrations in geometric settings.

Abstract

A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-K\"ahler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in $\bE^4\times HK_4$. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetry or no supersymmetry, depending on the time orientation.