Orbifold reduction and 2d (0,2) gauge theories

Abstract

We introduce Orbifold Reduction, a new method for generating 2d (0; 2) gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds. The new procedure generalizes dimensional reduction and orbifolding. In terms of T-dual con figurations, it generates brane brick models starting from brane tilings. Orbifold reduction provides an agile approach for generating 2d (0; 2) theories with a brane realization. We present three practical applications of the new algorithm: the connection between 4d Seiberg duality and 2d triality, a combinatorial method for generating theories related by triality and a 2d (0; 2) generalization of the Klebanov-Witten mass deformation.