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Brane Brick Models in the Mirror
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abstract
Brane brick models are Type IIA brane configurations that encode the $2d$ $\mathcal{N}=(0,2)$ gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how $2d$ $(0,2)$ triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is $n-1$ for a Calabi-Yau $n$-fold. This makes us conjecture the existence of a quadrality symmetry in $0d$. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of $2d$ $(0,2)$ theories in terms of 4-manifolds.
Forward citations
Cited by 4 Pith papers
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Abelian Orbifolds for Brane Brick Models
A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.
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Quiver BPS Indices from Crystal Profiles
Elliptic genera and lower-dimensional BPS indices equal discrete sums over molecule boundaries in crystals defined by Jeffrey-Kirwan residues, generalizing Nekrasov Young-diagram formulas.
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Quiver-Invariant Dualities between Brane Tilings
A tilting mutation of brane tilings yields distinct superpotentials on the same quiver with identical mesonic moduli space, equivalent to a sequence of Seiberg dualities.
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Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.
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