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 Dl-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.