Reconstructing conformal field theoretical compositions with Transformers

2026-05-01

AI Summary

This study addresses the highly combinatorial inverse problem of reconstructing constituent rational conformal field theories (RCFTs) from the low-energy spectrum of their tensor products. To tackle this challenge, the authors introduce, for the first time, a Transformer-based model that takes low-energy spectral data as input and incorporates central charges and affine Lie algebra labels as auxiliary features to effectively capture the structure of Wess–Zumino–Witten (WZW) model tensor products. The proposed method achieves 98% accuracy on the WZW reconstruction task and demonstrates strong generalization capabilities to unseen categories and RCFTs with larger central charges, significantly advancing the application of machine learning to inverse problems in conformal field theory.

Abstract

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.

Problem

• conformal field theory
• tensor product decomposition
• bulk reconstruction
• AdS/CFT
• low-energy spectrum

Innovation

• Transformers
• conformal field theory
• tensor product decomposition
• bulk reconstruction
• Wess-Zumino-Witten models