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Vortices, Q-balls and Domain Walls on Dielectric M2-branes
Arai, Masato,Montonen, Claus,Sasaki, Shin IOP Publishing Ltd 2009 Journal of high energy physics Vol.2009 No.3
We study BPS solitons in &calN; = 6 U(<I>N</I>) × U(<I>N</I>) Chern-Simons-matter theory deformed by an F-term mass. The F-term mass generically breaks &calN; = 6 supersymmetry down to &calN; = 2. At vacua, M2-branes are polarized into a fuzzy <I>S</I><SUP>3</SUP> forming a spherical M5-brane with topology <B>R</B><SUP>1,2</SUP> × <I>S</I><SUP>3</SUP>. The polarization is interpreted as Myers' dielectric effect caused by an anti-self-dual 4-form flux <I>T</I><SUB>4</SUB> in the eleven-dimensional supergravity. Assuming a polarized M2-brane configuration, the model effectively reduces to the well-known abelian Chern-Simons-Higgs model studied in detail by Jackiw-Lee-Weinberg. We find that the potential for the fuzzy <I>S</I><SUP>3</SUP> radius agrees with the one calculated from the M5-brane point of view at large <I>N</I>. This effective model admits not only BPS topological vortex and domain wall solutions but also non-topological solitons that keep 1/4 of the manifest &calN; = 2 supersymmetry. We also comment on the reduction of our configuration to ten dimensions.