Abstract
We derive the BPS equations satisfied by lump solitons in
(2+1)-dimensional sigma models with toric 8-dimensional
hyper-Kähler (HK8) 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 
1,2 × HK8 background. Using the
κ-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
HK8 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 
= 3 or
= 4 theory.
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