Superconformal field theories from crystal lattices

Abstract

We propose a brane configuration for the (2+1)d, $\mathcal{N}=2$ superconformal theories (CFT${}_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT${}_4$. The fundamental fields of the CFT${}_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and baryons.

4 pages, 4 figures, revtex; v2. references added, minor corrections

References in corpus (5)

• Deformations of conformal theories and non-toric quiver gauge theories
• Deformations of Toric Singularities and Fractional Branes
• Comments on Anomalies and Charges of Toric-Quiver Duals
• Global symmetries and 't Hooft anomalies in brane tilings
• New $Ad{S}_4\times X_7$ Geometries with $\mathcal{N}=6$ in M Theory

Cited by in corpus (29)

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• Counting Gauge Invariants: the Plethystic Program
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• Brane Tilings
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• Brane Tilings and M2 Branes
• Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries
• Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Towards M2-brane Theories for Generic Toric Singularities
• Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
• Quiver Chern-Simons theories and crystals
• N=4 Chern-Simons theories and wrapped M-branes in their gravity duals
• Phases of M2-brane Theories
• M2-brane Probe Dynamics and Toric Duality
• Higgsing M2-brane Theories
• Symmetries of Abelian Orbifolds
• AdS/CFT with Tri-Sasakian Manifolds
• Calabi-Yau Volumes and Reflexive Polytopes
• Chern-Simons: Fano and Calabi-Yau
• Probing AdS4/CFT3 proposals beyond chiral rings
• On nonsupersymmetric $\BC^4/\BZ_N$, tachyons, terminal singularities and flips
• Charges and homologies in AdS_4/CFT_3
• M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Klebanov-Witten flows in M-theory
• Quiver Chern-Simons theories and 3-algebra orbifolds
• Geometric free energy of toric AdS4/CFT3 models
• Hilbert Series of Bipartite Field Theories