Generative AI for brane configurations and coamoeba
Rak-Kyeong Seong · Physical review. D/Physical review. D. · 2025
We introduce a generative AI model to obtain type IIB brane configurations that realize toric phases of a family of 4 D N = 1 supersymmetric gauge theories. These 4 D N = 1 quiver gauge theories are world volume theories of a D3-brane probing a toric Calabi-Yau 3-fold. The type IIB brane configurations are given by the coamoeba projection of the mirror curve associated with the toric Calabi-Yau 3-fold. The shape of the mirror curve and its coamoeba projection, as well as the corresponding type IIB brane configuration and the toric phase of the 4 d N = 1 theory, all depend on the complex structure moduli parametrizing the mirror curve. We train a generative AI model, a conditional variational autoencoder (CVAE), that takes a choice of complex structure moduli as input and generates the corresponding coamoeba. This enables us not only to obtain a high-resolution representation of the entire phase space for a family of 4 D N = 1 theories corresponding to the same toric Calabi-Yau 3-fold, but also to continuously track the movements of the mirror curve and the branes wrapping the curve in the corresponding type IIB brane configurations during phase transitions associated with Seiberg duality.