Vortices, Q-balls and Domain Walls on Dielectric M2-branes

We study BPS solitons in N = 6 U(N) x U(N) Chern-Simons-matter theory deformed by an F-term mass. The F-term mass generically breaks N = 6 supersymmetry down to N = 2. At vacua, M2-branes are polarized into a fuzzy S3 forming a spherical M5-brane with topology R1,2 x S3. The polarization is interpreted as Myers' dielectric effect caused by an anti-self-dual 4-form flux T4 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 S3 radius agrees with the one calculated from the M5-brane point of view at large N. 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 N = 2 supersymmetry. We also comment on the reduction of our configuration to ten dimensions.