$3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories

TL;DR

The paper introduces '3d printing', an innovative algorithm that constructs 2d $ ext{(0,2)}$ gauge theories from 4d $ ext{(1,1)}$ theories, improving the process of analyzing complex Calabi-Yau geometries.

Contribution

It presents a novel 3d printing algorithm that simplifies generating 2d gauge theories from 4d theories, enabling analysis of more complex geometries.

Findings

Efficient generation of gauge theories for Calabi-Yau 4-folds.

Connection between triality and 3d printing methods.

First discussion on brane brick model consistency and reduction.

Abstract

We introduce $3d$ printing, a new algorithm for generating $2d$ $\mathcal{N}=(0, 2)$ gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using $4d$ $\mathcal{N}=1$ 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. $3d$ 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 $2d$ $\mathcal{N}=(0, 2)$ gauge theories, and the freedom in $3d$ printing given an underlying Calabi-Yau 4-fold. Finally, we present the first discussion of the consistency and reduction of brane brick models.