Generative AI for Brane Configurations and Coamoeba

TL;DR

This paper presents a generative AI model that produces Type IIB brane configurations for 4d N=1 supersymmetric gauge theories, enabling detailed exploration of phase spaces and transitions in toric Calabi-Yau geometries.

Contribution

It introduces a conditional variational autoencoder that generates coamoeba projections of mirror curves based on complex structure moduli, advancing the modeling of brane configurations.

Findings

High-resolution phase space representation for 4d N=1 theories

Continuous tracking of mirror curve movements during phase transitions

AI-generated brane configurations match theoretical expectations

Abstract

We introduce a generative AI model to obtain Type IIB brane configurations that realize toric phases of a family of 4d N=1 supersymmetric gauge theories. These 4d N=1 quiver gauge theories are worldvolume 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 4d N=1 theory, all depend on the complex structure moduli parameterizing 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 4d 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.