Machine-learning methods were first introduced in 2017 to compute the minimum volume of the Sasaki-Einstein base of a non-compact toric Calabi-Yau 3-fold. The worldvolume theories on D3-branes probing toric Calabi-Yau 3-folds realize a large family of 4d N=1 gauge theories, which are also realized by Type IIB brane configurations known as brane tilings. More recently, these machine-learning methods have been refined to yield explicit formulas for the volumes corresponding to toric Calabi-Yau 3-folds. Unsupervised learning techniques have also been developed to identify toric phases - distinct brane tilings, and hence distinct 4d N=1 gauge theories, associated with the same underlying Calabi-Yau geometry. This talk will review these developments and present a generative AI model trained to learn the correspondence between a toric Calabi-Yau 3-fold and its associated 4d N=1 gauge theory. Taking the complex-structure moduli of the Calabi-Yau mirror curve as input, the model generates the shape of the mirror curve. From this output, one can reconstruct both the underlying Type IIB brane configuration, encoded by a brane tiling, and the Lagrangian data of the corresponding gauge theory. By varying the complex-structure moduli, we further show that the trained model captures transitions between distinct brane tilings and their corresponding gauge theories, thereby providing a AI-generated description of phases and phase transitions under Seiberg duality.
https://arxiv.org/abs/2411.16033
https://arxiv.org/abs/2310.19276
https://arxiv.org/abs/2309.05702
https://arxiv.org/abs/1706.03346
https://arxiv.org/abs/1704.03462