用生成模型自动构建超对称量子场论的膜构型，揭示相变过程。
Generative AI for Brane Configurations and Coamoeba
- 基于条件变分自编码器，根据模参数生成镜曲线的共振象图
- 首次实现同一卡比-丘流形下4D超对称理论相空间的高分辨率建模
- 适用于研究塞伯格对偶引起的相变中膜结构演化
我们提出一种生成式AI模型，用于构建实现代数相的4d N=1超对称规范理论的Type IIB膜构型。这些4d N=1量子杨-米尔斯理论是探测卡比-丘3维流形的D3膜的世界体积理论。其对应膜构型由该流形的镜曲线的共振象投影决定。镜曲线及其共振象形状、以及对应的膜构型和理论代数相，均依赖于镜曲线所参数化的复结构模。我们训练了一个条件变分自编码器（CVAE），以复结构模为输入，生成对应的共振象。这不仅实现了对同一卡比-丘3维流形对应的一族4d N=1理论整个相空间的高分辨率表示，还能够连续追踪塞伯格对偶相关相变过程中镜曲线与环绕其的膜的运动轨迹。
原文摘要 · Abstract (English)
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.
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