Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers

TL;DR

This paper introduces brane brick models as a new Type IIA brane configuration that encodes 2d (0,2) gauge theories related to toric Calabi-Yau 4-folds, providing a combinatorial approach to connect gauge theories with geometries.

Contribution

It presents brane brick models as a novel framework for understanding 2d (0,2) gauge theories on D1-branes over toric Calabi-Yau 4-folds, including new combinatorial methods for geometry-gauge theory correspondence.

Findings

Brane brick models encode 2d (0,2) gauge theories on D1-branes.

New combinatorial procedures relate gauge theories to Calabi-Yau geometries.

Streamlined connection between gauge theories and probed geometries.

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 D1-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.