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

TL;DR

This paper constructs and analyzes half-BPS non-Abelian vortex solitons in the mass-deformed ABJM theory at both weak and strong coupling, revealing their moduli spaces and dual gravity descriptions.

Contribution

It provides the first detailed study of non-Abelian vortices in mass-deformed ABJM theory, including their moduli spaces and dual supergravity descriptions at strong coupling.

Findings

Vortices preserve six supersymmetries and break gauge symmetry to U(1) x U(1).

The vortex moduli space includes a CP^1 and a six-dimensional space at strong coupling.

The D0-brane mass matches the classical vortex mass, confirming the duality.

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.