2<i>d</i> (0, 2) gauge theories from branes: Recent progress in brane brick models

We discuss the realization of [Formula: see text] [Formula: see text] gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi–Yau 4-folds. These brane setups fully encode the infinite class of [Formula: see text] [Formula: see text] quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. We review various methods for efficiently generating Brane Brick Models. These algorithms are then used to construct [Formula: see text] [Formula: see text] gauge theories for the cones over all the smooth Fano 3-folds and two infinite families of Sasaki–Einstein 7-manifolds with known metrics.