3d printing of 2d N = (0,2) gauge theories

We introduce 3d printing, a new algorithm for generating 2 d N = (0, 2) gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using 4 d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds as starting points. Equivalently, this method produces brane brick models starting from brane tilings. 3 d printing represents a significant improvement with respect to previously available tools, allowing a straightforward determination of gauge theories for geometries that until now could only be tackled using partial resolution. We investigate the interplay between triality, an IR equivalence between different 2 d N = ( 0; 2) gauge theories, and the freedom in 3 d printing given an underlying Calabi-Yau 4-fold. Finally, we present the first discussion of the consistency and reduction of brane brick models.