Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers

Abstract

We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (generically) N=(0,2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given gauge theory and vice versa.

80 pages, 53 figures. v3: Minor clarification added. Published version

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• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Orbifold Reduction and 2d (0,2) Gauge Theories
• Quadrality for Supersymmetric Matrix Models
• Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models
• Higher Cluster Categories and QFT Dualities
• Calabi-Yau Volumes and Reflexive Polytopes
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• The Origin of Calabi-Yau Crystals in BPS States Counting
• 2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds
• Mass Deformations of Brane Brick Models
• Brane Brick Models for the Sasaki-Einstein 7-Manifolds Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2)
• Gauge origami and quiver W-algebras
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• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• Calabi-Yau Products: Graded Quivers for General Toric Calabi-Yaus
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• On the Classification of Duality Webs for Graded Quivers
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• "Lagrangian Disks" in M-theory
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• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Quiver Gauge Theories: Beyond Reflexivity
• 2d dualities from 4d
• Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
• An Overview of Crystals and Double Quiver Yangians
• Tetrahedron duality
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• Hilbert Series of Bipartite Field Theories
• Quiver-Invariant Dualities between Brane Tilings