BPS Vortices, $Q$-balls, and $Q$-vortices in $\mathcal{N}=6$} Chern-Simons Matter Theory

Abstract

We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed ABJM theories. For the undeformed case, we analyze the $\mathcal{N}=2$ BPS equations for U(2)$\times$U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouville- or Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U($N$)$\times$U($N$) gauge symmetry, we obtain some number of pairs of coupled differential equations from the $\mathcal{N}=1,2$ BPS equations, which can be reduced to the vortex equations in Maxwell-Higgs theory or Chern-Simons matter theories as special cases. We discuss the solutions. In $\mathcal{N}=3$ vortex equations Chern-Simons-type vortex equation is not allowed. We also show that $\mathcal{N}=\frac{5}{2},\frac{3}{2},\frac{1}{2}$ BPS equations are equivalent to those with higher integer supersymmetries.

38 pages, 1 figure

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• Partially Supersymmetric ABJM Theory with Flux

Cited by in corpus (1)

• Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k