Brane Brick Models in the Mirror
Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa

TL;DR
This paper uses mirror symmetry to systematically construct brane brick models for 2d (0,2) gauge theories on D1-branes probing toric Calabi-Yau 4-folds, revealing geometric dualities and conjecturing a new quadrality symmetry.
Contribution
It introduces a mirror symmetry approach to construct brane brick models from geometry and explores geometric realizations of dualities, including a conjecture of quadrality in 0d theories.
Findings
Mirror symmetry provides a systematic construction method.
Geometric transitions realize 2d (0,2) triality.
Conjecture of a quadrality symmetry in 0d theories.
Abstract
Brane brick models are Type IIA brane configurations that encode the 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 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 for a Calabi-Yau -fold. This makes us conjecture the existence of a quadrality symmetry in . Finally, we comment on how the M-theory lift of brane brick models connects to the…
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