Membrane solitons in eight-dimensional hyper-Kaehler backgrounds

TL;DR

This paper derives BPS equations for lump solitons in 2+1D sigma models with 8D hyper-Kähler targets, explores their M-theory realization, and discusses supersymmetry preservation and dualities.

Contribution

It introduces the BPS equations for solitons in hyper-Kähler backgrounds and analyzes their supersymmetry properties within M-theory and dual Hanany-Witten setups.

Findings

Solitons preserve half of the supersymmetry in the sigma model.

Discrepancy in supersymmetry preservation between low energy and full M-theory descriptions.

Toric HK8 manifolds are dual to D3-brane configurations with vortex interpretations.

Abstract

We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional sigma models with toric 8-dimensional hyper-K\"ahler (${HK}_8$) target spaces and check they preserve 1/2 of the supersymmetry. We show how these solitons are realised in M theory as M2-branes wrapping holomorphic 2-cycles in the $\bE^{1,2}\times {HK}_8$ background. Using the $\kappa$-symmetry of a probe M2-brane in this background we determine the supersymmetry they preserve, and note that there is a discrepancy in the fraction of supersymmetry preserved by these solitons as viewed from the low energy effective sigma model description of the M2-brane dynamics or the full M theory. Toric ${HK}_8$ manifolds are dual to a Hanany-Witten setup of D3-branes suspended between 5-branes. In this picture the lumps correspond to vortices of the three dimensional ${\mathcal N}=3$ or ${\mathcal N}=4$ theory.