# A Comprehensive Survey of Brane Tilings

## TL;DR

This paper provides a comprehensive classification of brane tilings associated with toric Calabi-Yau 3-folds up to a certain size, enhancing the understanding of gauge theories in string theory.

## Contribution

It offers the first complete classification of toric Calabi-Yau 3-folds with small toric diagrams and the corresponding brane tilings, expanding computational tools in the field.

## Key findings

- Classified toric Calabi-Yau 3-folds up to area 8.
- Developed efficient computational tools for brane tilings.
- Produced a comprehensive database of brane tilings.

## Abstract

An infinite class of $4d$ $\mathcal{N}=1$ gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi-Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to local model building in string phenomenology. Brane tilings fully encode the gauge theories on the D3-branes and have substantially simplified their connection to the probed geometries. The purpose of this paper is to push the boundaries of computation and to produce as comprehensive a database of brane tilings as possible. We develop efficient implementations of brane tiling tools particularly suited for this search. We present the first complete classification of toric Calabi-Yau 3-folds with toric diagrams up to area 8 and the corresponding brane tilings. This classification is of interest to both physicists and mathematicians alike.