Abelian-Higgs and Vortices from ABJM: towards a string realization of AdS/CMT

Abstract

We present ansätze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^{\alpha }$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to embed all the usual (multi-)vortex solutions of the latter into the ABJM model. By turning off the mass deformation at the level of the reduced model, we can also continuously deform to the massive ${\varphi }^4$ theory in the massless ABJM case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT correspondence as a consistent truncation of ABJM. In this context, the mass deformation parameter $\mu$ and a field VEV $<\varphi >$ act as $g$ and $g_c$ respectively, leading to a well-motivated AdS/CMT construction from string theory. To further this particular point, we propose a simple model for the condensed matter field theory that leads to an approximate description for the ABJM abelianization. Finally, we also find some BPS solutions to the mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending on a spherical M5-brane.

43 pages, latex, explanations added in the introduction, end of section 4, and on page 25

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Cited by in corpus (11)

• Particle-vortex and Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$/ABJM correspondence
• Penrose limits and spin chains in the GJV/CS-SYM duality
• Abelian Projections of the Mass-deformed ABJM theory and Weakly Curved Dual Geometry
• M5-branes in ABJM theory and Nahm equation
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Non-topological Vortex Configurations in the ABJM Model
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• N=2 Chern-Simons-Matter Theories Without Vortices
• Abelian reductions of deformed $\mathcal{N}=4$ SYM
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Open strings on D-branes from ABJM