Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation

Abstract

We present an embedding of the 3-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an $\mathcal{N}=6$, $U(N)\times U(N)$ Chern-Simons-matter theory (the ABJM model) by consistently truncating the latter to an abelian effective field theory encoding the collective dynamics of $\mathcal{O}(N)$ of the $\mathcal{O}(N^2)$ modes. In fact, depending on the VEV on one of the ABJM scalars, a mass deformation parameter $\mu$ and the Chern-Simons level number $k$, our abelianization prescription allows us to interpolate between the abelian Higgs model with its usual multi-vortex solutions and a ${\varphi }^4$ theory. We sketch a simple condensed matter model that reproduces all the salient features of the abelianization. In this context, the abelianization can be interpreted as giving a dimensional reduction from four dimensions.

4 pages, revtex; reference added, typo corrected; added clarifying paragraphs at end of introduction and on pages 3-4. Version accepted to PRL

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Lectures on Holographic Superfluidity and Superconductivity
• A Massive Study of M2-brane Proposals
• On M5-branes in N=6 Membrane Action
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

Cited by in corpus (11)

• Abelian-Higgs and Vortices from ABJM: towards a string realization of AdS/CMT
• 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
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Non-topological Vortex Configurations in the ABJM Model
• Generalized extremal branes in AdS/CMT and holographic superconductors
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• Abelian reductions of deformed $\mathcal{N}=4$ SYM
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Open strings on D-branes from ABJM