On the Classification of Brane Tilings

TL;DR

This paper introduces an efficient algorithm to generate all possible brane tilings, including inconsistent ones, significantly advancing the classification of these structures relevant for superconformal theories and string theory duals.

Contribution

The paper presents a new computational algorithm that systematically generates all brane tilings up to six superpotential terms, encompassing both consistent and inconsistent configurations.

Findings

Generated all brane tilings with up to 6 superpotential terms

Provided the most comprehensive collection of inconsistent brane tilings to date

Enhanced understanding of the landscape of brane tilings and their classifications

Abstract

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.