Machine Learning Toric Duality in Brane Tilings

TL;DR

This paper explores machine learning techniques to classify and analyze Seiberg dualities and toric phases in 4d $ mathcal{N}=1$ quantum field theories from D3-branes on toric Calabi-Yau 3-folds, achieving high accuracy in predictions.

Contribution

It introduces neural network models to classify Seiberg dual theories and predict toric phase properties, demonstrating effective application of ML in complex quantum field theory problems.

Findings

Neural network classifies Seiberg dual theories with R^2=0.988.

Residual architecture predicts toric phase space with mean absolute error 0.021.

Robustness of methods evaluated against perturbations in theory space.

Abstract

We apply a variety of machine learning methods to the study of Seiberg duality within 4d $\mathcal{N}=1$ quantum field theories arising on the worldvolumes of D3-branes probing toric Calabi-Yau 3-folds. Such theories admit an elegant description in terms of bipartite tessellations of the torus known as brane tilings or dimer models. An intricate network of infrared dualities interconnects the space of such theories and partitions it into universality classes, the prediction and classification of which is a problem that naturally lends itself to a machine learning investigation. In this paper, we address a preliminary set of such enquiries. We begin by training a fully connected neural network to identify classes of Seiberg dual theories realised on $\mathbb{Z}_m\times\mathbb{Z}_n$ orbifolds of the conifold and achieve $R^2=0.988$. Then, we evaluate various notions of robustness of our methods against perturbations of the space of theories under investigation, and discuss these results in terms of the nature of the neural network's learning. Finally, we employ a more sophisticated residual architecture to classify the toric phase space of the $Y^{6,0}$ theories, and to predict the individual gauged linear $\sigma$-model multiplicities in toric diagrams thereof. In spite of the non-trivial nature of this task, we achieve remarkably accurate results; namely, upon fixing a choice of Kasteleyn matrix representative, the regressor achieves a mean absolute error of $0.021$. We also discuss how the performance is affected by relaxing these assumptions.