Diagnosing Inconsistencies in 4d N=1 Gauge Theories with Explainable AI

Abstract

Brane tilings are bipartite graphs on a 2-torus that encode the Lagrangians of 4d N=1 supersymmetric gauge theories arising on D3-branes probing toric Calabi-Yau 3-folds. Among these bipartite graphs, only those that satisfy geometric consistency conditions correspond to well-behaved quantum field theories. We train a convolutional neural network (CNN) to distinguish geometrically consistent from inconsistent brane tilings directly from their Kasteleyn matrices. We study a family of 4d N=1 theories obtained by adding diagonal edges to the hexagonal faces of the brane tiling for the abelian orbifold C^3/Z_3 x Z_3, and find that the CNN identifies geometric inconsistency with high accuracy. For inconsistent brane tilings that can be rendered consistent by Higgsing a single bifundamental chiral field, we show that gradient-based saliency analysis can be used to localize the responsible chiral fields with accuracy well above a matched random baseline. These results demonstrate that explainable AI (XAI) can be used to identify local defects responsible for inconsistencies in supersymmetric gauge theories.