Non-Abelian Vortices at Weak and Strong Coupling in Mass Deformed ABJM Theory

Abstract

We find half-BPS vortex solitons, at both weak and strong coupling, in the N=6 supersymmetric mass deformation of ABJM theory with U(N) x U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Z_k quotient of the N=8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the mass deformed M2-brane theory. At weak coupling, the BPS vortices preserving six supersymmetries are found in the Higgs vacuum of the theory where the gauge symmetry is broken to U(1) x U(1). The classical vortex solitons break a colour-flavour locked global symmetry resulting in non-Abelian internal orientational moduli and a CP^1 moduli space of solutions. At strong coupling and large k, upon reduction to type IIA strings, the vortex moduli space and its action are computed by a probe D0-brane in the dual geometry. The mass of the D0-brane matches the classical vortex mass. However, the gravity picture exhibits a six dimensional moduli space of solutions, a section of which can be identified as the CP^1 we find classically, along with a Dirac monopole connection of strength k. It is likely that the extra four dimensions in the moduli space are an artifact of the strong coupling limit and of the supergravity approximation.

arXiv comment39 pages, 5 figures. v2 minor changes. v3 discussion added about fermionic zero modes

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• Renormalized Holographic Subregion Complexity under Relevant Perturbations
• Conductivity in the gravity dual to massive ABJM and the membrane paradigm
• Roton-phonon excitations in Chern-Simons matter theory at finite density
• Non-topological Vortex Configurations in the ABJM Model
• Holography of Massive M2-brane Theory with Discrete Torsion
• BPS Vortices, $Q$-balls, and $Q$-vortices in $\mathcal{N}=6$} Chern-Simons Matter Theory