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 N = 2 BPS equations for U(2)×U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouvilleor Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U(N )×U(N ) gauge symmetry, we obtain some number of pairs of coupled differential equations from the 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 N = 3 vortex equations Chern-Simons-type vortex equation is not allowed. We also show that N =

Dual localized objects from m-branes over ${{AdS}}_{4}\times {S}^{7}/{Z}_{k}$

“…Finally, in addition to the references quoted sofar on (mainly nonperturbative) studies in framework of AdS 4 /CFT 3 correspondence, here is a good place to mention some other related and recent works. For a study on various partially localized objects (monopoles, vortices, Q-balls and so on) in the ABJM model, look at [37] and references therein, and see [38] for studying the type IIB T-dual of the extended objects in the correspondence. To study localization techniques in supergravity in the current duality and context look at [39], and see [40] for a study of adding M5-branes in AdS 4 × Q 1,1,1 space-times and also look at [41] for an overview of exact (intersecting) solutions in M-theory.…”