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Membrane solitons in eight-dimensional hyper-Kaehler backgrounds

Ruben Portugues
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Abstract

We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional sigma models with toric 8-dimensional hyper-Kähler (${HK}_8$) 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 $κ$-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 ${HK}_8$ 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.

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Ruben Portugues. 2003-12-16. Membrane solitons in eight-dimensional hyper-Kaehler backgrounds. https://doi.org/10.1088/1126-6708%2F2004%2F03%2F051

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