用Transformer从低能谱重构二维共形场论的张量积结构
Reconstructing conformal field theoretical compositions with Transformers
- 基于低能谱信息，用Transformer学习共形场论的张量积构成
- 在WZW模型张量积上实现98%的构造成分恢复准确率
- 方法可泛化到更高中心荷和未见类别的共形场论
我们研究了使用Transformer根据二维有理共形场论（RCFT）的低能谱重构其张量积的构成。该任务因组合性质而具有挑战性。构成理论由中心荷和仿射李代数标签表征。我们在基于Wess-Zumino-Witten模型构建的张量积理论中实现了98%的成分恢复准确率。进一步证明，通过添加少量域外样本，该方法可推广至中心荷更大的共形场论以及未见过的RCFT类别。结果表明，Transformer在此任务中表现有效，并为AdS/CFT中的全息重建提供了新工具。
原文摘要 · Abstract (English)
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The constituent theories are characterized by their central charges and affine Lie algebra labels. We achieve 98% accuracy in recovering the constituents of tensor products theories constructed from Wess-Zumino-Witten models. We further demonstrate that our method generalizes to CFTs with larger central charge and unseen classes of RCFTs by adding a small number of out-of-domain examples. Our results show that transformers are effective at this task and point towards a new tool for bulk reconstruction in AdS/CFT.
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