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Brane brick models are Type IIA brane configurations that encode the 2d 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.


This article was originally published in the Journal for High Energy Physics, availabe at doi:10.1007/JHEP02(2017)106.

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0).

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