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.
Related
- Vacuum Structure of Maximally Supersymmetric Two-Dimensional Gauge Theories
- Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights
- Elliptic spin Ruijsenaars-Schneider integrable models from 5d 𝒩=1 gauge theories
- Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories
- Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories
BibTeX
@misc{lee2026diagnosing,
title = {{Diagnosing Inconsistencies in 4d N=1 Gauge Theories with Explainable AI}},
author = {Seong-Jin Lee and Rak-Kyeong Seong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21867},
eprint = {2609.21867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21867},
}
RIS
TY - UNPB
TI - Diagnosing Inconsistencies in 4d N=1 Gauge Theories with Explainable AI
AU - Seong-Jin Lee
AU - Rak-Kyeong Seong
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21867
UR - https://arxiv.org/abs/2609.21867
AB - 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.
ER -