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arXiv · 1609.01723

Brane Brick Models in the Mirror

Sebastian Franco·Sangmin Lee·Rak-Kyeong Seong·Cumrun Vafa
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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.

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Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa. 2016-09-06. Brane Brick Models in the Mirror. https://doi.org/10.1007/jhep02(2017)106

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